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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 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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Functions of Omega-Bounded Type in the Halfplane
In this chapter, some Riesz-type descriptive representations are established for several Nevanlinna-Djrbashian-type classes of functions...
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A new result on boundedness of the Riesz potential in central Morrey–Orlicz spaces
We improve our results on boundedness of the Riesz potential in the central Morrey–Orlicz spaces and the corresponding weak-type version. We also...
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Some New Discrete Copson-Type Inequalities Involving a Generalized Riesz Mean Operator
In this paper, we establish some new weighted discrete inequalities containing a generalized Riesz mean operator. The obtained inequalities hold for...
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Vector-valued McShane and strong McShane integrals with the Alexiewicz norm and its Riesz representation theorems
This article discusses McShane and strong McShane integration theory in the class of vector-valued functions endowed with the Alexiewicz norm, their...
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Łoskot-Rudnicki’s Inequality and General Relative Entropy Inequality for Cauchy Problems Preserving Positivity
The Generalized Relative Entropy inequality is a ubiquitous property in mathematical models applied in physics or biology. In spite of its...
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Riesz-type Inequalities and Overdetermined Problems for Triangles and Quadrilaterals
We consider Riesz-type nonlocal interaction energies over polygons. We prove the analog of the Riesz inequality in this discrete setting for...
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Bernstein Spaces, Sampling, and Riesz-Boas Interpolation Formulas in Mellin Analysis
The goal of the chapter is to consider Bernstein-Mellin subspaces in the Lebesgue-Mellin spaces and establishing for functions in these subspaces new...
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Weakly Compact Sets and Riesz Representation Theorem in Musielak Sequence Spaces
In this work, we give some criteria of the weakly compact sets and a representation theorem of Riesz’s type in Musielak sequence spaces using the...