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The class Bpfor weighted generalized Fourier transform inequalities

Chokri Abdelkefi, Mongi Rachdi (2015)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

In the present paper, we prove weighted inequalities for the Dunkl transform (which generalizes the Fourier transform) when the weights belong to the well-known class Bp. As application, we obtain the Pitt’s inequality for power weights.

The class of convolution operators on the Marcinkiewicz spaces

Ka-Sing Lau (1981)

Annales de l'institut Fourier

Let 𝒯 X denote the operator-norm closure of the class of convolution operators Φ μ : X X where X is a suitable function space on R . Let r p be the closed subspace of regular functions in the Marinkiewicz space p , 1 p < . We show that the space 𝒯 r p is isometrically isomorphic to 𝒯 L p and that strong operator sequential convergence and norm convergence in 𝒯 r p coincide. We also obtain some results concerning convolution operators under the Wiener transformation. These are to improve a Tauberian theorem of Wiener on 2 .

The generalizations of integral analog of the Leibniz rule on the G-convolutions.

Semyon B. Yakubovich, Yurii F. Luchko (1991)

Extracta Mathematicae

An integral analog of the Leibniz rule for the operators of fractional calculus was considered in paper [1]. These operators are known to belong to the class of convolution transforms [2]. It seems very natural to try to obtain some new integral analog of the Leibniz rule for other convolution operators. We have found a general method for constructing such integral analogs on the base of notion of G-convolution [4]. Several results obtained by this method are represented in this article.

Twisted spherical means in annular regions in n and support theorems

Rama Rawat, R.K. Srivastava (2009)

Annales de l’institut Fourier

Let Z ( Ann ( r , R ) ) be the class of all continuous functions f on the annulus Ann ( r , R ) in n with twisted spherical mean f × μ s ( z ) = 0 , whenever z n and s > 0 satisfy the condition that the sphere S s ( z ) Ann ( r , R ) and ball B r ( 0 ) B s ( z ) . In this paper, we give a characterization for functions in Z ( Ann ( r , R ) ) in terms of their spherical harmonic coefficients. We also prove support theorems for the twisted spherical means in n which improve some of the earlier results.

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