Maximal functions and subordination for operator groups.

Blower, Gordon (2002) Maximal functions and subordination for operator groups. Proceedings of the Edinburgh Mathematical Society, 45 (1). pp. 27-42. ISSN 0013-0915

Abstract

Let E be a UMD Banach space and L a positive and self-adjoint operator in L^2 of Laplace type such that the imaginary powers L^{-it} form a C_0 group of exponential growth on L^p(E). Suppose that G is holomorphis inside and on the boundary os a suitable sector. Then G(tL) defines a bounded family of linear operators on L^p(E); the maximal operator f->sup | G(tL)f| os bounded on the domain of log L. These hypotheses hold for the maximal solution operators for the heat, wave and Schroedinger operators, and for Cesaro sums.