Open AccessFlat singular integrals in product domains
Author(s) -
Ahmad Al-Salman
Publication year - 2004
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil0418001a
Subject(s) - mathematics , convexity , bounded function , product (mathematics) , kernel (algebra) , singular integral , pure mathematics , mathematical analysis , geometry , integral equation , financial economics , economics
In this paper, we study singular integrals on product domains with kernels in L(logL)2(Sn?1?Sm?1) supported by surfaces of revolutions. We prove that our operators are bounded on Lp under certain convexity assumption on the surfaces. Also, in this paper we prove that the convexity assumption is not necessary for the L boundedness to hold. Moreover, additional related results are presented. Our condition on the kernel is known to be optimal.