Strongly Singular Convolution Operators and their Commutators on Variable Herz-type Hardy Spaces

Document Type : Original Article

Authors

Aissa Djeriou ¹

Rabah Heraiz ²

¹ Laboratory of Functional Analysis and Geometry of Spaces, Faculty of Mathematics and Computer science, University of M'sila, University Pole, Road Bourdj Bou Arreiridj, M'sila 28000, Algeria.

² Laboratory of Functional Analysis and Geometry of Spaces, Faculty of Mathematics and Computer Science, University of M'sila, University Pole, Road Bourdj Bou Arreiridj, M'sila 28000, Algeria.

10.22034/kjm.2025.489254.3375

Abstract

The aim of this paper is to prove that strongly singular convolution operators are bounded from $H\dot{K}_{{p(\cdot )}}^{{\alpha (\cdot )},q{(\cdot )}}(\mathbb{R}^{n})$ to $\dot{K}_{{p(\cdot )}}^{{\alpha (\cdot)},q{(\cdot )}}(\mathbb{R}^{n})$ when $\alpha \left( 0\right) =n-n/p\left(0\right) $ and $\alpha _{\infty }=n-n/p_{\infty }$. Also, the boundedness of their commutators from the inhomogeneous Herz-type Hardy spaces to the inhomogeneous Herz spaces has been obtained.

Keywords

Herz-type Hardy spaces

atom

variable exponent

strongly singular convolution operators

commutator

Subjects

• 42 Harmonic analysis on Euclidean spaces

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