Rough singular integrals on product spaces

Abstract

We study the mapping properties of singular integral operators defined by mappings of finite type. We prove that such singular integral operators are bounded on the Lebesgue spaces under the condition that the singular kernels are allowed to be in certain block spaces.2000 Mathematics Subject Classification: 42B20, 42B15, 42B25.

Maximal functions associated to surfaces of revolution on product domains

“…The following lemma which is Theorem 2.6 in [8] will be used to establish L p estimates of maximal functions on product domains. [8].)…”

“…[8].) Letm,n, M, N ∈ N, B > 1, a, b 2, α, β > 0, and let L : Rn → R N and Q : Rm → R M be linear transformations.…”

Marcinkiewicz integral operators along twisted surfaces

“…In order to prove the boundedness of the concerned maximal functions, we have the following lemma which is an analog of Theorem 2.5 in [8]:…”