Journals / Turkish Journal of Mathematics / 2005 / Cilt: 29 - Sayı: 3
On Rough Singular Integrals Along Surfaces on Product Domains
- Pages
- 275–285
- DOI
- —
Abstract
In this paper, we study a class of singular integrals along surfaces on product domains with kernels in L(log L)2(Sn-1 \times Sm-1). We formulate a general theorem concerning the Lp boundedness of these operators. As a consequence of this theorem we establish Lp estimates of several classes of operators whose Lp boundedness in the one parameter setting is known. The condition L(log L)2(Bn-1 \times Sm-1) is known to be an optimal size condition
Özet
In this paper, we study a class of singular integrals along surfaces on product domains with kernels in L(log L)2(Sn-1 \times Sm-1). We formulate a general theorem concerning the Lp boundedness of these operators. As a consequence of this theorem we establish Lp estimates of several classes of operators whose Lp boundedness in the one parameter setting is known. The condition L(log L)2(Bn-1 \times Sm-1) is known to be an optimal size condition