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Related papers: Sobolev embeddings for kinetic Fokker-Planck equat…

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We introduce Herz-Sobolev spaces, which unify and generalize the classical Sobolev spaces. We will give a proof of the Sobolev-type embedding for these function spaces. All these results generalize the classical results on Sobolev spaces.…

Functional Analysis · Mathematics 2022-10-25 Douadi Drihem

Parabolic integro-differential Kolmogorov equations with different space-dependent operators are considered in H\"{o}lder-type spaces defined by a scalable L\'{e}vy measure. Probabilistic representations are used to prove continuity of the…

Probability · Mathematics 2018-10-04 Fanhui Xu

In a recent work of the author, a parabolic extension of the elliptic Ogawa type inequality has been established. This inequality is originated from the Brezis-Gallouet-Wainger logarithmic type inequalities revealing Sobolev embeddings in…

Functional Analysis · Mathematics 2009-08-25 Hassan Ibrahim

One proves the well-posedness in the Sobolev space H^{-1} of nonlinear Fokker-Planck equations with singular drifts.Applications to existence of strong solutions to McKean-Vlasov equations are given.

Analysis of PDEs · Mathematics 2025-06-03 Viorel Barbu

Sobolev-type inequalities have been extensively studied in the frameworks of real-valued functions and non-commutative $\mathbb{L}_p$ spaces, and have proven useful in bounding the time evolution of classical/quantum Markov processes, among…

Quantum Physics · Physics 2019-05-06 Hao-Chung Cheng , Min-Hsiu Hsieh

We investigate potential spaces associated with Jacobi expansions. We prove structural and Sobolev-type embedding theorems for these spaces. We also establish their characterizations in terms of suitably defined fractional square functions.…

Classical Analysis and ODEs · Mathematics 2015-12-31 Bartosz Langowski

We survey a few trace theorems for Sobolev spaces on $N$-dimensional Euclidean domains. We include known results on linear subspaces, in particular hyperspaces, and smooth boundaries, as well as less known results for Lipschitz boundaries,…

Functional Analysis · Mathematics 2019-12-12 Pier Domenico Lamberti , Luigi Provenzano

This paper first proves the existence, uniqueness and regularity of the solution to a class of linear backward parabolic equations on Carnot tori, namely the periodic linear parabolic equation on Carnot groups. Such groups are…

Analysis of PDEs · Mathematics 2026-02-06 Yiming Jiang , Yawei Wei , Yiyun Yang

In this paper, we study the sharp Poincar\'e inequality and the Sobolev inequalities in the higher order Lorentz--Sobolev spaces in the hyperbolic spaces. These results generalize the ones obtained in \cite{Nguyen2020a} to the higher order…

Functional Analysis · Mathematics 2020-01-14 Van Hoang Nguyen

We prove Strichartz estimates on general flat d-torus for arbitrary d. Using these estimates, we prove local wellposedness for the cubic nonlinear Schr\"odinger equations in appropriate Sobolev spaces. In dimensions 2 and 3, we prove…

Analysis of PDEs · Mathematics 2008-09-29 F. Catoire , W. -M. Wang

We solve the Stechkin problem about approximation of generally speaking unbounded hypersingular integral operators by bounded ones. As a part of the proof, we also solve several related and interesting on their own problems. In particular,…

Functional Analysis · Mathematics 2022-06-06 Vladyslav Babenko , Oleg Kovalenko , Nataliia Parfinovych

The scope of this text is to study a process that induces another proof of the Spectral Embedding Theorem: that any densely defined symmetric operator can be extended by a multiplication operator through an embedding of the Hilbert space…

Functional Analysis · Mathematics 2026-05-29 Fabrice Nonez

In this article, we introduce and study capacities related to nonlocal Sobolev spaces, with focus on spaces corresponding to zero-order nonlocal operators. In particular, we prove Hardy-type inequalities to obtain Sobolev embeddings and use…

Analysis of PDEs · Mathematics 2024-10-15 Tomasz Grzywny , Julia Lenczewska

We introduce a priori Sobolev-space error estimates for the solution of nonlinear, and possibly parametric, PDEs using Gaussian process and kernel based methods. The primary assumptions are: (1) a continuous embedding of the reproducing…

Numerical Analysis · Mathematics 2023-05-10 Pau Batlle , Yifan Chen , Bamdad Hosseini , Houman Owhadi , Andrew M Stuart

We prove an error estimate for a Lie-Trotter splitting operator associated to the Schrodinger-Poisson equation in the semiclassical regime, when the WKB approximation is valid. In finite time, and so long as the solution to a compressible…

Numerical Analysis · Mathematics 2013-12-23 Rémi Carles

We obtain a general concept of triplet of Hilbert spaces with closed (unbounded) embeddings instead of continuous (bounded) ones. The construction starts with a positive selfadjoint operator $H$, that is called the Hamiltonian of the…

Functional Analysis · Mathematics 2025-11-04 Petru Cojuhari , Aurelian Gheondea

We establish foundational properties of fractional operators on Lie groups of homogeneous type. We prove embedding theorems for the associated Sobolev-type spaces.

Analysis of PDEs · Mathematics 2026-01-22 Nicola Garofalo , Annunziata Loiudice , Dimiter Vassilev

In this paper, we define the fractional Orlicz-Sobolev spaces, and we prove some important results of these spaces. The main result is to show the continuous and compact embedding for these spaces. As an application, we prove the existence…

Analysis of PDEs · Mathematics 2018-08-01 Elhoussine Azroul , Abdelmoujib Benkirane , Mohammed Srati

We provide martingale analogs of weakly cancelling differential operators and prove a Sobolev-type embedding theorem for these operators in the martingale setting.

Classical Analysis and ODEs · Mathematics 2019-09-04 Dmitriy Stolyarov

We consider certain Littlewood-Paley operators and prove characterization of some function spaces in terms of those operators. When treating weighted Lebesgue spaces, a generalization to weighted spaces will be made for H\"ormander's…

Classical Analysis and ODEs · Mathematics 2016-01-14 Shuichi Sato