On Derivatives, Riesz Transforms and Sobolev Spaces for Fourier–Bessel expansions
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DOI: 10.1007/s00041-021-09896-1
Abstract: We study the problem of an appropriate choice of derivatives associated with discrete Fourier-Bessel expansions. We introduce a new so-called essential measure Fourier-Bessel setting, where the relevant derivative is simply the ordinary derivative. Then we… read more here.
Keywords: derivatives riesz; fourier bessel; bessel expansions; sobolev spaces ... See more keywords
Sharp weighted norm inequalities for singular integrals with non–smooth kernels
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DOI: 10.1007/s00209-019-02416-4
Abstract: In this paper, we prove the sharp weighted bound for certain singular integrals which have non-smooth kernels and do not belong to the class of standard Calderón–Zygmund operators. Our assumptions are weaker than those known… read more here.
Keywords: integrals non; singular integrals; smooth kernels; non smooth ... See more keywords
A1-Regularity and Boundedness of Riesz Transforms in Banach Lattices of Measurable Functions
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DOI: 10.1007/s10958-018-3698-z
Abstract: Let X be a Banach lattice of measurable functions on ℝn × Ω having the Fatou property. We show that the boundedness of all Riesz transforms Rj in X is equivalent to the boundedness of… read more here.
Keywords: measurable functions; boundedness riesz; riesz transforms; boundedness ... See more keywords
Riesz transforms for the Weinstein operator
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DOI: 10.1080/10652469.2017.1358713
Abstract: ABSTRACT In this paper we study the Riesz transforms related to the Weinstein operators . We develop for a theory that runs parallel to the one for the Euclidean Riesz Transform. It is proved that… read more here.
Keywords: transforms weinstein; weinstein operator; riesz; riesz transforms ... See more keywords
Weak Factorizations of the Hardy Space H 1(ℝ n ) in Terms of Multilinear Riesz Transforms
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DOI: 10.4153/cmb-2017-033-9
Abstract: Abstract This paper provides a constructive proof of the weak factorization of the classical Hardy space ${{H}^{1}}({{\mathbb{R}}^{n}})$ in terms of multilinear Riesz transforms. As a direct application, we obtain a new proof of the characterization… read more here.
Keywords: multilinear riesz; hardy space; riesz transforms; terms multilinear ... See more keywords