On the Boundedness of Marcinkiewicz Integrals on Variable Exponent Herz-type Hardy Spaces

Rabah Heraiz

doi:10.5666/KMJ.2019.59.2.259

Article

KYUNGPOOK Math. J. 2019; 59(2): 259-275

Published online June 23, 2019

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

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Abstract

The aim of this paper is to prove that Marcinkiewicz integral operators are bounded from K˙p(·)α(·),q(·)(ℝn) to K˙p(·)α(·),q(·)(ℝn) when the parameters α(·), p(·) and q(·) satisfies some conditions. Also, we prove the boundedness of μ on variable Herz-type Hardy spaces HK˙p(·)α(·),q(·)(ℝn).

Keywords: Herz spaces, Herz-type Hardy spaces, variable exponent, HardyLittlewood maximal operator, Marcinkiewicz integral operators.