الملخص الإنجليزي
In this work, we discuss the L p boundedness of several classes of integral operators with homogeneous kernels on product domains. We establish L p boundedness
of singular and Marcinkiewicz integral operators on product domains when their
kernels are in L(log L)2(Sn−1 × Sm−1). We also proved the Lp boundedness of
Marcinkiewicz integral operators on product domains provided that the kernels
satisfy Grafakos-Stevanov’s size conditions. Furthermore, we study the L
p boundedness of a class of singular integral operators along twisted surfaces with kernels
belonging to the space L(log L)
2
(S
n−1 × S
m−1
). Finally, we prove some weighted
norm inequality of a class of Marcinkiewicz integral operators on product domains
along various surfaces provided that the kernels are in L(log L)
2
(S
n−1 × S
m−1
).
