Marcinkiewicz integrals on product spaces

H. Al-Qassem; A. Al-Salman; L. C. Cheng; Y. Pan

doi:10.4064/sm167-3-4

Marcinkiewicz integrals on product spaces

H. Al-Qassem^*, A. Al-Salman, L. C. Cheng, Y. Pan

^*Corresponding author for this work

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

26 Citations (Scopus)

Abstract

We prove the L^p boundedness of the Marcinkiewicz integral operators μΩ on ℝⁿ¹ × ... × ℝ^nk under the condition that Ω∈L(log L) ^k/2(struck S sign ^n1-1 × ... × struck S sign ^nk-1). The exponent k/2 is the best possible. This answers an open question posed in [?].

Original language	English
Pages (from-to)	227-234
Number of pages	8
Journal	Studia Mathematica
Volume	167
Issue number	3
DOIs	https://doi.org/10.4064/sm167-3-4
Publication status	Published - 2005
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)

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abstract = "We prove the Lp boundedness of the Marcinkiewicz integral operators μΩ on ℝn1 × ... × ℝnk under the condition that Ω∈L(log L) k/2(struck S sign n1-1 × ... × struck S sign nk-1). The exponent k/2 is the best possible. This answers an open question posed in [?].",

author = "H. Al-Qassem and A. Al-Salman and Cheng, {L. C.} and Y. Pan",

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AU - Al-Qassem, H.

AU - Al-Salman, A.

AU - Cheng, L. C.

AU - Pan, Y.

PY - 2005

Y1 - 2005

N2 - We prove the Lp boundedness of the Marcinkiewicz integral operators μΩ on ℝn1 × ... × ℝnk under the condition that Ω∈L(log L) k/2(struck S sign n1-1 × ... × struck S sign nk-1). The exponent k/2 is the best possible. This answers an open question posed in [?].

AB - We prove the Lp boundedness of the Marcinkiewicz integral operators μΩ on ℝn1 × ... × ℝnk under the condition that Ω∈L(log L) k/2(struck S sign n1-1 × ... × struck S sign nk-1). The exponent k/2 is the best possible. This answers an open question posed in [?].

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DO - 10.4064/sm167-3-4

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JF - Studia Mathematica

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ER -

Marcinkiewicz integrals on product spaces

Abstract

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