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Multiscale Weak Compactness in Metric Spaces
The aim of this paper is to provide a useful tool for a better understanding of the approach proposed in [11] to extend to the setting of metric...
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Non-Linear Mixed Norm Spaces for Sobolev Embeddings in the Critical Case
We prove a sharp version of the endpoint Sobolev embedding in the context of non-linear function classes with mixed norms.
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A simple proof of Hardy’s inequality in a limiting case
In this short note, we provide a simple proof of Hardy’s inequality in a limiting case. In the proof we do not need any symmetrization technique such...
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Equivalence between Pólya–Szegő and relative capacity inequalities under rearrangement
The transformations of functions acting on sublevel sets that satisfy a Pólya–Szegő inequality are characterized as those being induced by...
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Hodge-type Decomposition for Time-dependent First-order Parabolic Operators with Non-constant Coefficients: The Variable Exponent Case
In this paper we present a Hodge-type decomposition for variable exponent spaces. More concretely, we address some time-dependent parabolic...
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Some Weighted Inequalities of Trudinger–Moser Type
We discuss some extensions of the Trudinger–Moser inequality in a special case of weighted Sobolev spaces
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Sobolev Trace Theorem and the Dirichlet Problem in the Unit Disk
We give a direct and elementary proof for the trace theorem in L p -based Sobolev spaces, when the domain is the unit disk. We also consider the...
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B σ-Campanato Estimates for Commutators of Calderón–Zygmund Operators
In the earlier papers [16, 19], the Bσ-function spaces were introduced for the purpose of unifying central Morrey spaces, λ-central mean oscillation...
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A Characterization of Two-Weight Trace Inequalities for Positive Dyadic Operators in the Upper Triangle Case
Two-weight trace inequalities for positive dyadic operators are characterized in terms of discrete Wolff’s potentials in the upper triangle case.
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An alternative proof of the Aubin–Lions lemma
Using a generalized version of the Weyl–Riesz criterion for compactness of subsets of Lebesgue–Bochner spaces, we present in this short note an...
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Symmetry Breaking of Extremals for the Caffarelli-Kohn-Nirenberg Inequalities in a Non-Hilbertian Setting
We provide an explicit necessary condition to have that no extremal for the best constant in the Caffarelli-Kohn-Nirenberg inequality is radially...
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A geometric criterion for compactness of invariant subspaces
Let M be a non-compact homogeneous Riemannian manifold, and let Ω be a compact subgroup of isometries of M . We show, under general conditions, that...
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Sobolev spaces, Lebesgue points and maximal functions
In this note, we study boundedness of a large class of maximal operators in Sobolev spaces that includes the spherical maximal operator. We also...
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Direct form seminorms arising in the theory of interpolation by Hankel translates of a basis function
Certain spaces of functions which arise in the process of interpolation by Hankel translates of a basis function, as developed by the authors...
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Higher-Order Multilinear Poincaré and Sobolev Inequalities in Carnot Groups
The notions of higher-order weighted multilinear Poincaré and Sobolev inequalities in Carnot groups are introduced. As an application, weighted...
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Weighted L p -estimates for Elliptic Equations with Measurable Coefficients in Nonsmooth Domains
We obtain a global weighted L p estimate for the gradient of the weak solutions to divergence form elliptic equations with measurable coefficients in...