Characterizations of the Sobolev space H1 on the boundary of a strongly Lipschitz domain in 3‐D: Characterizations of the Sobolev space \(\mathrm{H}^1\) on the boundary of a strongly Lipschitz domain in 3-D

Authors: Nathanael Skrepek

Source: Mathematische Nachrichten. 298:1342-1355

Subject Terms: Mathematics - Functional Analysis, tangential gradients, Mathematics - Analysis of PDEs, 46E35, 46E36, 47F99, tangential traces, Lipschitz domains, Sobolev spaces, FOS: Mathematics, Lipschitz boundaries, Sobolev spaces and other spaces of ''smooth' functions, embedding theorems, trace theorems, Functional Analysis (math.FA), Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/2304.06386

Matrix-weighted Besov-type and Triebel–Lizorkin-type spaces I: $$A_p$$-dimensions of matrix weights and $$\varphi $$-transform characterizations: Matrix-weighted Besov-type and Triebel-Lizorkin-type spaces. I: \(A_p\)-dimensions of matrix weights and \(\varphi\)-transform characterizations

Authors: Fan Bu, Tuomas Hytönen, Dachun Yang, Wen Yuan

Source: Mathematische Annalen. 391:6105-6185

Subject Terms: Mathematics - Functional Analysis, Maximal functions, Littlewood-Paley theory, FOS: Mathematics, Primary 46E35, Secondary 47A56, 42B25, 42C40, 42B35, Nontrigonometric harmonic analysis involving wavelets and other special systems, Sobolev spaces and other spaces of ''smooth' functions, embedding theorems, trace theorems, Function spaces arising in harmonic analysis, Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones), Functional Analysis (math.FA)

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Access URL: http://arxiv.org/abs/2304.00292

Calderón–Zygmund theory for strongly coupled linear system of nonlocal equations with Hölder-regular coefficient: Calderón-Zygmund theory for strongly coupled linear system of nonlocal equations with Hölder-regular coefficient

Authors: Mengesha, Tadele, Schikorra, Armin, Seesanea, Adisak, Yeepo, Sasikarn

Source: Advances in Calculus of Variations. 18:421-438

Subject Terms: Mathematics - Analysis of PDEs, Second-order elliptic systems, Calderon-Zygmund, elliptic systems, nonlocal PDE, Pseudodifferential operators, Sobolev spaces and other spaces of ''smooth' functions, embedding theorems, trace theorems, regularity theory, Fractional partial differential equations

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Access URL: http://arxiv.org/abs/2401.01886

A clustering theorem in fractional Sobolev spaces

Authors: Fatma Gamze Düzgün, Antonio Iannizzotto, Vincenzo Vespri

Source: Annales Fennici Mathematici; Vol. 50 No. 1 (2025); 243–252
Annales Fennici Mathematici; Vol 50 Nro 1 (2025); 243–252

Subject Terms: regularity, Mathematics - Analysis of PDEs, Smoothness and regularity of solutions to PDEs, Clustering, fractional Sobolev spaces, regularity, FOS: Mathematics, Sobolev spaces and other spaces of ''smooth' functions, embedding theorems, trace theorems, Fractional partial differential equations, fractional Sobolev spaces, 35R11, 46E35, 35B65, Clustering, clustering, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/2305.19965
https://afm.journal.fi/article/view/161328

Local and global Dunkl–Morrey-type spaces: Local and global Dunkl-Morrey-type spaces

Authors: Shi, M., Zhao, N., Liu, Y.

Source: Annals of Functional Analysis. 16

Subject Terms: Hardy spaces, Maximal functions, Littlewood-Paley theory, Singular and oscillatory integrals (Calderón-Zygmund, etc.), fractional maximal operators, local Morrey-type spaces, Dunkl-type generalized translation, Function spaces arising in harmonic analysis, Sobolev spaces and other spaces of ''smooth' functions, embedding theorems, trace theorems, \(H^p\)-spaces

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Access URL: https://zbmath.org/8036318
https://doi.org/10.1007/s43034-025-00425-5

On the stability estimate for the sharp second order uncertainty principle

Authors: Anh Tuan Duong, Van Hoang Nguyen

Source: Calculus of Variations and Partial Differential Equations. 64

Subject Terms: Inequalities involving derivatives and differential and integral operators, Inequalities for sums, series and integrals, Sobolev spaces and other spaces of ''smooth' functions, embedding theorems, trace theorems

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Access URL: https://zbmath.org/8032672
https://doi.org/10.1007/s00526-025-02988-6

A sharp higher order Sobolev embedding

Authors: Raul Hindov, Shahaf Nitzan, Jan‐Fredrik Olsen, Eskil Rydhe

Source: Mathematika. 71

Subject Terms: Mathematics - Functional Analysis, sharp estimate, extremal function, FOS: Mathematics, higher order, Sobolev spaces and other spaces of ''smooth' functions, embedding theorems, trace theorems, Sobolev embedding, Functional Analysis (math.FA)

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Access URL: http://arxiv.org/abs/2411.10201
https://zbmath.org/8012235
https://doi.org/10.1112/mtk.70012

Harris’ Criterion and Hardy Inequalities on Graphs: Harris' criterion and Hardy inequalities on graphs

Authors: Simon Murmann, Marcel Schmidt

Source: Integral Equations and Operator Theory. 97

Subject Terms: Distance in graphs, path pseudo metrics, Metric Geometry (math.MG), 01 natural sciences, Planar graphs, geometric and topological aspects of graph theory, Functional Analysis (math.FA), Mathematics - Functional Analysis, Mathematics - Metric Geometry, Sobolev spaces, discrete graphs, FOS: Mathematics, Inequalities for sums, series and integrals, 0101 mathematics, Sobolev spaces and other spaces of ''smooth' functions, embedding theorems, trace theorems

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Access URL: http://arxiv.org/abs/2303.07092
https://zbmath.org/8037015
https://doi.org/10.1007/s00020-025-02794-x

Compactness in Banach function spaces: Poincaré and Friedrichs inequalities

Authors: Bilal Bilalov, Eminaga Mamedov, Yonca Sezer, Natavan Nasibova

Source: Rendiconti del Circolo Matematico di Palermo Series 2. 74

Subject Terms: additive-invariant, Friedrichs inequality, Poincaré inequality, Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals, Inequalities involving derivatives and differential and integral operators, Banach-Sobolev spaces, rearrangement-invariant, compactness, Sobolev spaces and other spaces of ''smooth' functions, embedding theorems, trace theorems, Compactness in Banach (or normed) spaces, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

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Access URL: https://zbmath.org/7975320
https://doi.org/10.1007/s12215-024-01172-7

Multiple normalized solutions for Choquard equation involving the biharmonic operator and competing potentials in ℝN: Multiple normalized solutions for Choquard equation involving the biharmonic operator and competing potentials in \(\mathbb{R}^N\)

Authors: Shuaishuai Liang, Jiaying Ma, Shaoyun Shi, Yueqiang Song

Source: Bulletin of Mathematical Sciences, Vol 15, Iss 01 (2025)

Subject Terms: Variational methods for second-order elliptic equations, Quasilinear elliptic equations, QA1-939, variational methods, Lusternik–Schnirelmann category, Sobolev spaces and other spaces of ''smooth' functions, embedding theorems, trace theorems, Choquard equation, biharmonic operator, Lusternik-Schnirelmann category, normalized solutions, Mathematics

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Access URL: https://zbmath.org/8037534
https://doi.org/10.1142/s1664360724500176
https://doaj.org/article/7225726880464ee7b314a41578979c6b

Embedding and Duality of Matrix-weighted Modulation Spaces: Embedding and duality of matrix-weighted modulation spaces

Authors: Wang, Shengrong, Guo, Pengfei, Xu, Jingshi

Source: Taiwanese Journal of Mathematics. 29

Subject Terms: Mathematics - Functional Analysis, embedding, Duality and reflexivity in normed linear and Banach spaces, modulation space, FOS: Mathematics, duality, matrix weight, Sobolev spaces and other spaces of ''smooth' functions, embedding theorems, trace theorems, Functional Analysis (math.FA)

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Access URL: http://arxiv.org/abs/2405.15171
https://zbmath.org/7977965
https://doi.org/10.11650/tjm/240905

Besov spaces in operator theory

Authors: Peller, Vladimir V.

Source: Russian Mathematical Surveys. 79:1-52

Subject Terms: Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.), Research exposition (monographs, survey articles) pertaining to operator theory, triple operator integrals, Perturbation theory of linear operators, Mathematics - Complex Variables, Lipschitz (Hölder) classes, power bounded operators, injective tensor products, double operator integrals, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), 47B35, 30H25, 46E35, 47B10, 47A55, 60G10, 47A60, 46M05, Mathematics - Functional Analysis, Mathematics - Spectral Theory, Schatten-von Neumann classes, Mathematics - Classical Analysis and ODEs, Besov spaces, Linear operators on function spaces (general), self-adjoint operators, Toeplitz operators, Hankel operators, Wiener-Hopf operators, perturbations of linear operators, Sobolev spaces and other spaces of ''smooth' functions, embedding theorems, trace theorems, projective tensor products, Mathematics - Probability, Hankel operators, Schur multipliers

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Access URL: http://arxiv.org/abs/2402.09853
https://zbmath.org/7891391
https://doi.org/10.4213/rm10140e

The continuous quaternion wavelet transform on distribution spaces

Authors: Drema Lhamu, Aparna Das, Sunil Kumar Singh, Awniya Kumar

Source: Rendiconti del Circolo Matematico di Palermo Series 2. 74

Subject Terms: quaternions, continuous quaternion wavelet transform, Besov spaces and \(Q_p\)-spaces, Integral transforms in distribution spaces, Sobolev spaces and other spaces of ''smooth' functions, embedding theorems, trace theorems, Sobolev space, Besov space

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Access URL: https://zbmath.org/7971729
https://doi.org/10.1007/s12215-024-01180-7

The octonionic ripplet transforms: a mathematical perspective

Authors: Kumar, Awniya, Singh, Sunil Kumar, Singh, Sheo Kumar

Source: Journal of Pseudo-Differential Operators and Applications. 16

Subject Terms: General integral transforms, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, Nontrigonometric harmonic analysis involving wavelets and other special systems, distribution spaces, Sobolev spaces and other spaces of ''smooth' functions, embedding theorems, trace theorems, octonion-valued functions, ripplet transform, functions space

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Access URL: https://zbmath.org/7962351
https://doi.org/10.1007/s11868-024-00661-8

Existence and Mass Collapse of Standing Waves for Equation with General Potential and Nonlinearities: Existence and mass collapse of standing waves for equation with general potential and nonlinearities

Authors: Su, Yu, Shi, Hongxia, Yang, Jie

Source: Qualitative Theory of Dynamical Systems. 24

Subject Terms: dipolar quantum gases, Variational methods applied to PDEs, mass collapse, Schrödinger equation, Integro-differential operators, Sobolev spaces and other spaces of ''smooth' functions, embedding theorems, trace theorems, Choquard equation, ground states, Fractional partial differential equations, standing waves, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

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Equivalence of the Weighted Fractional Sobolev Space on a Disk with Characterization by the Decay Rate of Fourier–Jacobi Coefficients and K-Interpolation: Daniel Potts

Authors: V. J. Ervin

Source: Journal of Fourier Analysis and Applications. 30

Subject Terms: Fourier coefficients, Fourier series of functions with special properties, special Fourier series, Jacobi polynomials, spherical harmonics, fractional Laplacian, 0101 mathematics, Sobolev spaces and other spaces of ''smooth' functions, embedding theorems, trace theorems, weighted Sobolev spaces, 01 natural sciences

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On the study of some non-coercive elliptic equations in anisotropic weighted Sobolev spaces

Authors: Belayachi, Mohammed, Bouzelmate, Arij, Hjiaj, Hassane, Raiss, Inssaf

Subject Terms: Variational methods for second-order elliptic equations, Anisotropic weighted Sobolev spaces, renormalized solution, degenerate coercivity, non-coercive elliptic problems, anisotropic weighted Sobolev spaces, Nonlinear elliptic equations, Sobolev spaces and other spaces of ''smooth' functions, embedding theorems, trace theorems

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Access URL: https://zbmath.org/8014750
https://doi.org/10.34874/prsm.mjpaa-vol10iss2.2347

On the sharp constant in the Bianchi–Egnell stability inequality: On the sharp constant in the Bianchi-Egnell stability inequality

Authors: König, Tobias

Source: Bulletin of the London Mathematical Society. 55:2070-2075

Subject Terms: Mathematics - Analysis of PDEs, Bianchi-Egnell inequality, Sobolev inequality, FOS: Mathematics, Inequalities involving derivatives and differential and integral operators, 0101 mathematics, Sobolev spaces and other spaces of ''smooth' functions, embedding theorems, trace theorems, 01 natural sciences, fractional exponents, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/2210.08482

Solutions for fractional $p(x,\cdot )$-Kirchhoff-type equations in $\mathbb{R}^{N}$: Solutions for fractional \(p(x, \cdot)\)-Kirchhoff-type equations in \(\mathbb{R}^N\)

Authors: Wan, Lili

Source: Journal of Inequalities and Applications. 2024

Subject Terms: Boundary value problems for PDEs with pseudodifferential operators, Variational methods for higher-order elliptic equations, fractional \(p(x, \cdot)\)-Kirchhoff-type equations, mountain pass lemma, symmetric mountain pass lemma, Sobolev spaces and other spaces of ''smooth' functions, embedding theorems, trace theorems, Fractional partial differential equations

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Access URL: https://zbmath.org/8034402
https://doi.org/10.1186/s13660-024-03204-3

Trace principle for Riesz potentials on Herz-type spaces and applications

Authors: M. Ashraf Bhat, G. Sankara Raju Kosuru

Source: Journal of Inequalities and Applications, Vol 2024, Iss 1, Pp 1-13 (2024)

Subject Terms: Adams' trace inequality, 31C15, 26A33, 42B35, 46E35, Potentials and capacities on other spaces, Functional Analysis (math.FA), Mathematics - Functional Analysis, Fractional derivatives and integrals, QA1-939, Riesz potential, FOS: Mathematics, Herz spaces, Sobolev inequalities, Function spaces arising in harmonic analysis, Sobolev spaces and other spaces of ''smooth' functions, embedding theorems, trace theorems, Mathematics

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Access URL: http://arxiv.org/abs/2403.05929
https://zbmath.org/8034392
https://doi.org/10.1186/s13660-024-03192-4
https://doaj.org/article/f0ae2b9029d644c6afaab15dd81924cc