On the L2 boundedness of parametric Marcinkiewicz integral operator

Ahmad Al-Salman

doi:10.1016/j.jmaa.2010.09.062

On the L² boundedness of parametric Marcinkiewicz integral operator

Ahmad Al-Salman^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

17 Citations (Scopus)

Abstract

In this paper, we derive a multiplier formula for Hörmander's parametric Marcinkiewicz integral operator. As a consequence, we prove the optimality of the kernel size condition L(logL)^1/2(S^n-1) as well as the optimality of the Block size condition.

Original language	English
Pages (from-to)	745-752
Number of pages	8
Journal	Journal of Mathematical Analysis and Applications
Volume	375
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2010.09.062
Publication status	Published - Mar 15 2011

Keywords

Block spaces
Marcinkiewicz integrals
Parametric Marcinkiewicz integrals
Singular integrals

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1016/j.jmaa.2010.09.062

Cite this

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abstract = "In this paper, we derive a multiplier formula for H{\"o}rmander's parametric Marcinkiewicz integral operator. As a consequence, we prove the optimality of the kernel size condition L(logL)1/2(Sn-1) as well as the optimality of the Block size condition.",

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AB - In this paper, we derive a multiplier formula for Hörmander's parametric Marcinkiewicz integral operator. As a consequence, we prove the optimality of the kernel size condition L(logL)1/2(Sn-1) as well as the optimality of the Block size condition.

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KW - Parametric Marcinkiewicz integrals

KW - Singular integrals

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