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In this paper, we introduce a class of maximal functions along twisted surfaces in $\mathbb{R}^{n}\mathbb{\times R}^{m}$ of the form $$\{(\phi (\left\vert v\right\vert )u, \varphi (\left\vert u\right\vert )v):(u,v)\in \mathbb{R}^{n}\mathbb{\times R}^{m}\}.$$ We prove $L^{p}$ bounds when the kernels lie in the space $L^{q}(\mathbb{S}^{n-1}\mathbb{\times S}^{m-1})$. As a consequence, we establish the $L^{p}$ boundedness for such class of operators provided that the kernels are in $L\log L(\mathbb{S}^{n-1}\mathbb{ \times S}^{m-1})$ or in the Block spaces $B_{q}^{0,0}\left( \mathbb{S}^{n-1} \mathbb{\times S}^{m-1}\right) (q>1)$.
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참고문헌 (19)
참고문헌 신청
Hussain AL-QASSEM / 2002 / Lp boundedness for singular integrals with rough kernels on product domains / Hokkaido Mathematical Journal 31(3):555~613
Ahmad Al-Salman / 2005 / Maximal operators with rough kernels on product domains / Journal of Mathematical Analysis and Applications 311(1):338~351
Ahmad Al-Salman / 2008 / Maximal functions along surfaces on product domains / Analysis Mathematica 34(3):163~175
Ahmad Al-Salman / 2021 / Singular integral operators on product domains along twisted surfaces / Frontiers of Mathematics in China 16(1):13~28
Ahmad Al-Salman / 2002 / Integral Operators of Marcinkiewicz Type / Journal of Integral Equations and Applications 14(4):343~354
Ahmad Al-Salman / 2005 / Maximal operators with rough kernels on product domains / Journal of Mathematical Analysis and Applications 311(1):338~351
Ahmad Al-Salman / 2008 / Maximal functions along surfaces on product domains / Analysis Mathematica 34(3):163~175
Ahmad Al-Salman / 2021 / Singular integral operators on product domains along twisted surfaces / Frontiers of Mathematics in China 16(1):13~28
Ahmad Al-Salman / 2002 / Integral Operators of Marcinkiewicz Type / Journal of Integral Equations and Applications 14(4):343~354
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