Article
KYUNGPOOK Math. J. 2019; 59(2): 259-275
Published online June 23, 2019
Copyright © Kyungpook Mathematical Journal.
On the Boundedness of Marcinkiewicz Integrals on Variable Exponent Herz-type Hardy Spaces
Rabah Heraiz
Department of Mathematics, Laboratory of Functional Analysis and Geometry of Spaces, M’sila University, P. O. Box 166, M’sila 28000, Algeria
e-mail : heraizrabeh@yahoo.fr and rabah.heraiz@univ-msila.dz
Received: March 22, 2018; Revised: November 2, 2018; Accepted: December 6, 2018
Abstract
The aim of this paper is to prove that Marcinkiewicz integral operators are bounded from
Keywords: Herz spaces, Herz-type Hardy spaces, variable exponent, HardyLittlewood maximal operator, Marcinkiewicz integral operators.
1. Introduction and Preliminaries
Function spaces with variable exponent are being actively studied not only in the field of real analysis but also in partial differential equations and in applied mathematics. The theory of function spaces with variable exponents has rapidly made progress in the last three decades.
For 0
Given Ω ∈ Lip
where
The Marcinkiewicz integral
where
It is well known that the operator
Recently, the boundedness of Marcinkiewicz integral operators
The purpose of this paper is to generalize some results concerning Marcinkiewicz integral operators
The subset of variable exponents with range [1,∞) is denoted by
3. Variable Herz Estimate of Marcinkiewicz Integral Operators
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