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Lp ESTIMATES FOR A ROUGH MAXIMALOPERATOR ON PRODUCT SPACES

Lp ESTIMATES FOR A ROUGH MAXIMAL OPERATOR ON PRODUCT SPACES

Hussain Mohammed Al-Qassem
대한수학회 (The Korean Mathematical Society)|2005.05|대한수학회지 (Journal of the KMS)|제42권 제3호|pp. 405-434

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Abstract

We establish appropriate Lp estimates for a class of maximal operators S(°)­ on the product space Rn &pound; Rm when ­lacks regularity and 1 · ° · 2. Also, when ° = 2; we prove the Lp (2 · p < 1) boundedness of S(2)whenever ­ is a function in a certain block space B(0;0) q (Sn¡1 &pound; Sm¡1) (for some q > 1). Moreover, we show that the condition ­ 2 B(0;0) q (Sn¡1 &pound; Sm¡1) is nearly optimal in the sense that the operator S(2) may fail to be bounded on L2 if the condition ­ 2 B(0;0)q (Sn¡1 &pound; Sm¡1) is replaced by the weaker conditions ­ 2 B(0;") q (Sn¡1&pound;Sm¡1) for any ¡1 < " < 0

참고문헌 (14)

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관련 논문AI추천

Weighted Lp Estimates for a Rough Maximal OperatorH. M. Al-Qassem경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2005 · 제45권 제2호Lp Boundedness for Singular IntegralOperators with (log ) Kernels on Product SpacesHussain Al-Qassem, Mohammed Ali경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2006 · 제46권 제3호A Note on Marcinkiewicz Integral Operators on Product DomainsAhmad Al-Salman, Badriya Al-Azri경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2023 · 제63권 제4호Boundedness of multiple Marcinkiewicz integral operators with rough kernelsHuoxiong Wu대한수학회 · 대한수학회지2006 · 제43권 제3호Endpoint Estimates for Maximal Commutators inNon-homogeneous SpacesDachun Yang, Guoen Hu, Yan Meng대한수학회 · 대한수학회지2007 · 제44권 제4호Boundedness for Multilinear Littlewood-PaleyOperators on Certain Hardy SpacesLanzhe Liu경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2006 · 제46권 제3호

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