Generalized area operators on L^p({ℝ}^n)

Abstract

We introduce the generalized area operators by using nonnegative measures defined on upper half-spaces {ℝ}_{+}^{n+\mathrm{1}}. The characterization of the boundedness and compactness of the generalized area operator from L^p({ℝ}^n) to L^q({ℝ}^n) is investigated in terms of s-Carleson measures with 1<p, q<+∞. In the case of p = q = 1, the weak type estimate is also obtained.

Keywords

{ℝ}^n)Space')">L^p({ℝ}^n)Space / area operator / s-Carleson measure

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Higher Education Press and Springer-Verlag Berlin Heidelberg