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Full-Text Articles in Physical Sciences and Mathematics
Rough Singular Integrals Along Submanifolds Of Finite Type On Product Domains, Hussain Al-Qassem
Rough Singular Integrals Along Submanifolds Of Finite Type On Product Domains, Hussain Al-Qassem
Turkish Journal of Mathematics
We establish the L^p boundedness of singular integrals on product domains with rough kernels in L(log L)^2 and are supported by subvarieties.
Rough Oscillatory Singular Integral Operators-Ii, Ahmad Al-Salman, Ali A. Al-Jarrah
Rough Oscillatory Singular Integral Operators-Ii, Ahmad Al-Salman, Ali A. Al-Jarrah
Turkish Journal of Mathematics
In this paper, we study certain classes of oscillatory singular integral operators with kernels in Llog L(S^{n-1}) which is known to be the most desirable size condition for the L^{p} boundedness to hold. We prove that such operators are bounded on L^{p}. Our results extend and improve previously known results. Variations of our approach in this paper can be applied to handle more general oscillatory singular integral operators. This concludes by indicating a variety of results that can be obtained.