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Hardy–Sobolev Inequalities For Riesz Potentials Of Functions In Orlicz Spaces
We establish a Hardy–Sobolev inequality for Riesz potentials of functions in Orlicz spaces.
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On the Theory of Spaces of Generalized Bessel Potentials
We define the weighted Dirichlet integral and show that this integral can be represented by a multidimensional generalized shift. The corresponding...
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Riesz potentials and Sobolev-type inequalities in Orlicz-Morrey spaces of an integral form
Our aim is to give Sobolev-type inequalities for Riesz potentials of functions in Orlicz-Morrey spaces of an integral form over non-doubling metric...
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On the maximal singular integral with Riesz potentials
We investigate the maximal singular integral with Riesz potentials and give a short proof of its estimates through a result from Duoandikoetxea and...
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On Generalized Bessel Potentials and Perfect Functional Completions
AbstractThe class of generalized Bessel potentials is the main object of study in this paper. The generalized Bessel potential is a negative real...
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ON BOUNDEDNESS OF THE GENERALIZED RIESZ POTENTIAL IN LOCAL MORREY-TYPE SPACES
For all admissible values of the numerical parameters sharp sufficient conditions on the functional parameters are obtained ensuring the boundedness...
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Asymptotic Analysis for the Generalized Langevin Equation with Singular Potentials
We consider a system of interacting particles governed by the generalized Langevin equation (GLE) in the presence of external confining potentials,...
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d-Modified Riesz Potentials on Central Campanato Spaces
Recently, we defined the d-modified Riesz potentials $${\tilde...
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Two-weighted estimates for p-adic Riesz potential and its commutators on Morrey–Herz spaces
In this paper, we study the boundedness of p -adic Riesz potential on two-weighted Morrey–Herz spaces with both power weight and Muckenhoupt weight....
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Theory of generalized Bessel potential space and functional completion
The article’s objective is to present norms based on weighted Dirichlet integrals in the space of generalized Bessel potentials. The weighted...
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Classical Solutions of the Equation of Local Fluctuations of Riesz Gravitational Fields and their Properties
We consider a pseudodifferential equation involving the Riesz operator of fractional differentiation, which is a natural generalization of the...
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Generalized Orlicz-Type Slice Spaces, Extrapolation and Applications
We introduce a class of generalized Orlicz-type Auscher—Mourgoglou slice space, which is a special case of the Wiener amalgam. We prove versions of...
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New Gaussian Riesz transforms on variable Lebesgue spaces
We give sufficient conditions on the exponent p : ℝ d → [1, ∞) for the boundedness of the non-centered Gaussian maximal function on variable Lebesgue...
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On Flett potentials associated with the Laplace–Bessel differential operator
This article introduces new anisotropic wavelet-type transforms generated by the Laplace–Bessel differential operator. Two components generate these...
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Dimension-free Lp-estimates for vectors of Riesz transforms in the rational Dunkl setting
In this article, we prove a dimension-free upper bound for the L p -norms of the vector of Riesz transforms in the rational Dunkl setting. Our main...
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On the boundedness of B-maximal commutators, commutators of B-Riesz potentials and B-singular integral operators in modified B-Morrey spaces
In this paper we consider the generalized shift operator associated to the Laplace–Bessel differential operator Δ B and investigate B-maximal...