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On (Fejér-)Riesz type inequalities, Hardy–Littlewood type theorems and smooth moduli
The purpose of this paper is to develop some methods to study (Fejér-)Riesz type inequalities, Hardy–Littlewood type theorems and smooth moduli of...
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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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Anisotropic Fractional Gagliardo-Nirenberg, Weighted Caffarelli-Kohn-Nirenberg and Lyapunov-type Inequalities, and Applications to Riesz Potentials and p-sub-Laplacian Systems
In this paper we prove the fractional Gagliardo-Nirenberg inequality on homogeneous Lie groups. Also, we establish weighted fractional...
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Riesz–Kolmogorov Type Compactness Criteria in Function Spaces with Applications
We present forms of the classical Riesz–Kolmogorov theorem for compactness that are applicable in a wide variety of settings. In particular, our...
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Weak type (1, 1) of the Riesz transform on some direct product manifolds with exponential volume growth
In this paper, we are concerned with the Riesz transform on the direct product manifold ℍ n × M , where ℍ n is the n -dimensional real hyperbolic space...
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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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Riesz transforms and commutators in the Dunkl setting
In this paper we characterise the pointwise size and regularity estimates for the Dunkl Riesz transform kernel involving both the Euclidean metric...
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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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Almost Everywhere Convergence of Bochner–Riesz Means on Hardy–Sobolev Spaces
We investigate the convergence of Bochner–Riesz means on Hardy–Sobolev spaces. The relation between the smoothness imposed on functions and the rate...
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The Bochner–Riesz Problem: An Old Approach Revisited
We show that the recent techniques developed to study the Fourier restriction problem apply equally well to the Bochner–Riesz problem. This is...
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Asymptotics of k-nearest Neighbor Riesz Energies
We obtain new asymptotic results about systems of N particles governed by Riesz interactions involving k -nearest neighbors of each particle as
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A Bessel Analog of the Riesz Composition Formula
We provide an elementary derivation of the Bessel analog of the celebrated Riesz composition formula and use the former to effortlessly derive the...
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Riesz–Zygmund Means and Approximation in Variable Exponent Grand Spaces
In the paper, the estimates of generalized modulus of smoothness and best approximation in variable exponent grand Lebesgue spaces in terms of norms...
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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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Riesz Transform Estimates: Part I
In this chapter, we characterize the range of exponents p for...
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