Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Maximal functions and subordination for operator groups.
AU - Blower, Gordon
N1 - AMS 2000 classification 47D03; 42B25; 47D09 The final, definitive version of this article has been published in the Journal, Proceedings of the Edinburgh Mathematical Society, 45 (1), pp 27-42 2002, © 2002 Cambridge University Press.
PY - 2002/2
Y1 - 2002/2
N2 - 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.
AB - 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.
KW - maximal functions
KW - transference
KW - UMD Banach spaces
U2 - 10.1017/S0013091500000535
DO - 10.1017/S0013091500000535
M3 - Journal article
VL - 45
SP - 27
EP - 42
JO - Proceedings of the Edinburgh Mathematical Society
JF - Proceedings of the Edinburgh Mathematical Society
SN - 0013-0915
IS - 1
ER -