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초록· 키워드
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Under the rough kernels $\Omega$ belonging to the block spaces $B_{r}^{0,q}({\rm S}^{n-1})$ or the radial Grafakos-Stefanov kernels $W\mathcal{F}_\beta({\rm S}^{n-1})$ for some $r,\,\beta>1$ and $q\leq 0$, the boundedness and continuity were proved for two classes of rough maximal singular integrals and maximal operators associated to polynomial mappings on the Triebel-Lizorkin spaces and Besov spaces, complementing some recent boundedness and continuity results in \cite{LXY1,LXY2}, in which the authors established the corresponding results under the conditions that the rough kernels belong to the function class $L(\log L)^{\alpha}({\rm S}^{n-1})$ or the Grafakos-Stefanov class $\mathcal{F}_\beta({\rm S}^{n-1})$ for some $\alpha\in[0,1]$ and $\beta\in(2,\infty)$.
목차
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참고문헌 (36)
참고문헌 신청
Khadija Al-Balushi / 2014 / Certain L^p bounds for rough singular integrals / Journal of Mathematical Inequalities 8(4):803~822
H. M. Al-Qassem / 2012 / Boundedness of rough integral operators on Triebel-Lizorkin spaces / Publicacions Matemàtiques 56(2):261~277
A. Al-Salman / 2002 / Singular integrals with rough kernels in L log L(S n−1) / J. London Math. Soc 66(2):153~174
Yanping Chen / 2010 / Rough singular integrals supported on submanifolds / Journal of Mathematical Analysis and Applications 368(2):677~691
Jiecheng Chen / 2002 / Singular integral operators on function spaces / Journal of Mathematical Analysis and Applications 276(2):691~708
H. M. Al-Qassem / 2012 / Boundedness of rough integral operators on Triebel-Lizorkin spaces / Publicacions Matemàtiques 56(2):261~277
A. Al-Salman / 2002 / Singular integrals with rough kernels in L log L(S n−1) / J. London Math. Soc 66(2):153~174
Yanping Chen / 2010 / Rough singular integrals supported on submanifolds / Journal of Mathematical Analysis and Applications 368(2):677~691
Jiecheng Chen / 2002 / Singular integral operators on function spaces / Journal of Mathematical Analysis and Applications 276(2):691~708
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