L^pBOUNDS FOR THE PARABOLIC LITTLEWOOD-PALEY OPERATOR ASSOCIATED TO SURFACES OF REVOLUTION

Abstract

Abstract. In this paper the authors study the L p boundedness for parabolic Littlewood-Paley operatorwhereand Ω satisfies a condition introduced by Grafakos and Stefanov in [6]. The result in the paper extends some known results.

Generalized parabolic Marcinkiewicz integrals associated with polynomial compound curves with rough kernels

“…under various conditions on the kernel functions has been carried out by many researchers (see, for example, refs. [25][26][27][28][29][30]).…”

Parabolic Marcinkiewicz Integrals Associated to Polynomials Compound Curves and Extrapolation

“…Moreover, it follows from Wang, Chen and Yu's work [25] (also see [3,19]) that M Ω is of type (p, p) for 2β/(2β − 1) < p < 2β if Ω ∈ F β (S n−1 ) for some β > 1, where…”

Parabolic Marcinkiewicz integrals on product spaces and extrapolation

“…Subsequently, the study of the L p boundedness of under various conditions on the function has been studied by many authors (see for example [3][4][5][6][7]). …”