Parabolic Marcinkiewicz integrals on product spaces and extrapolation

Abstract

Abstract:In this paper, we study the the parabolic Marcinkiewicz integral M 1 ; 2 ;h on product domains R n R m .n; m 2/. L p estimates of such operators are obtained under weak conditions on the kernels. These estimates allow us to use an extrapolation argument to obtain some new and improved results on parabolic Marcinkiewicz integral operators.

Boundedness of Generalized Parametric Marcinkiewicz Integrals Associated to Surfaces

“…Subsequently, the investigation of the L p boundedness of the parametric Marcinkiewicz integrals under very various conditions on Ω, φ, and h has attracted the attention of many authors. For a sampling of studies of such operators, the readers are referred to [6][7][8][9][10][11][12][13][14] and the references therein.…”

Estimates for Generalized Parabolic Marcinkiewicz Integrals with Rough Kernels on Product Domains

“…(iv) For the case µ = 2 and ∈ (1, 2], the range of p in Theorem 3 is better than the range obtained in Theorem 1.2 in [8] in which the authors proved the L p boundedness of G…”

“…). Later on, the authors of [8] improved the results in [7]. In fact, they proved the L p boundedness of G…”

“…In the view of the results in [8] regarding the boundedness of the parabolic Marcinkiewicz operator G…”

Generalized Parabolic Marcinkiewicz Integral Operators Related to Surfaces of Revolution

“…(2),c Ω,ψ,g under very various conditions on the kernels attractted the attention of many mathematicians. For relevant results, we advice the readers to consult [8][9][10][11][12][13][14][15][16], among others.…”