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Map**s Generating Embedding Operators in Orlicz-Sobolev Spaces
We study embedding operators on Orlicz–Sobolev spaces generated by the composition rule. Using the composition operators we consider embeddings of...
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A New Proof of the Geometric Sobolev Embedding for Generalised Kolmogorov Operators
In this note we revisit nonlocal isoperimetric inequalities and the related embeddings for Besov spaces adapted to a class of Hörmander operators of...
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On a weighted Sobolev embedding on the upper half-space in a borderline case
The purpose of this paper is to establish some weighted Sobolev inequalities, which are the borderline cases of the Sobolev embedding on the upper...
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Sobolev embeddings in infinite dimensions
In this paper, we study Sobolev spaces in infinite dimensions and the corresponding embedding theorems. Our underlying spaces are ℓ r for r ∈ [1, ∞),...
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Sobolev spaces
Sobolev spaces were introduced by Sergei Lvovich Sobolev in the 1930s, and have since been widely embraced and developed by other mathematicians....
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A note on the embedding theorems for Sobolev-Lorentz spaces
In this work, we take non-traditional approaches in the literature to give new proofs of Sobolev-type inequalities for Lorentz spaces in two cases
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An embedding theorem for anisotropic fractional Sobolev spaces
Mixed-norm estimates are useful in studying solutions to dispersive equations. In this paper, we introduce the anisotropic fractional Sobolev spaces...
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Sobolev Spaces
Contact and friction problems, as well as many other problems involving elliptic partial differential equations and some specific boundary...
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Hardy–Sobolev–Rellich, Hardy–Littlewood–Sobolev and Caffarelli–Kohn–Nirenberg Inequalities on General Lie Groups
In this paper, we establish a number of geometrical inequalities such as Hardy, Sobolev, Rellich, Hardy–Littlewood–Sobolev,...
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Sobolev Spaces
A locally integrable function has a weak derivative of order α when its derivative of order α in the sense of distributions is represented by a...
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Bourgain, Brezis and Mironescu theorem for fractional Sobolev spaces with variable exponents
A Bourgain–Brezis–Mironescu-type theorem for fractional Sobolev spaces with variable exponents is established for sufficiently regular functions. We...
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Grand Sobolev Spaces on Metric Measure Spaces
We study the properties of the so-called grand Sobolev spaces on a metric measure space. The introduction of the spaces is motivated by the available...
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Strengthened Fractional Sobolev Type Inequalities in Besov Spaces
The purpose of this article is twofold. The first is to strengthen fractional Sobolev type inequalities in Besov spaces via the classical Lorentz...
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Global Compactness, Subcritical Approximation of the Sobolev Quotient, and a Related Concentration Result in the Heisenberg Group
We investigate some effects of the lack of compactness in the critical Sobolev embedding in the Heisenberg group.
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Logarithmic Sobolev Inequalities of Fractional Order on Noncommutative Tori
In this paper, we prove a version of the logarithmic Sobolev inequality of fractional order on noncommutative n-tori for any dimension...
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Fractional Sobolev Spaces with Kernel Function on Compact Riemannian Manifolds
In this paper, a new class of Sobolev spaces with kernel function satisfying a Lévy-integrability-type condition on compact Riemannian manifolds is...
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Inclusion Relations Among Fractional Orlicz-Sobolev Spaces and a Littlewood-Paley Characterization
Embeddings among fractional Orlicz-Sobolev spaces with different smoothness are characterized. In particular, besides recovering standard embeddings...