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**Maximal functions and subordination for operator groups.** / Blower, Gordon.

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Blower, G 2002, 'Maximal functions and subordination for operator groups.', *Proceedings of the Edinburgh Mathematical Society*, vol. 45, no. 1, pp. 27-42. https://doi.org/10.1017/S0013091500000535

Blower, G. (2002). Maximal functions and subordination for operator groups. *Proceedings of the Edinburgh Mathematical Society*, *45*(1), 27-42. https://doi.org/10.1017/S0013091500000535

Blower G. Maximal functions and subordination for operator groups. Proceedings of the Edinburgh Mathematical Society. 2002 Feb;45(1):27-42. https://doi.org/10.1017/S0013091500000535

@article{2e0ad01e414f454ca7f3f91c829f218f,

title = "Maximal functions and subordination for operator groups.",

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.",

keywords = "maximal functions, transference, UMD Banach spaces",

author = "Gordon Blower",

note = "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, {\textcopyright} 2002 Cambridge University Press.",

year = "2002",

month = feb,

doi = "10.1017/S0013091500000535",

language = "English",

volume = "45",

pages = "27--42",

journal = "Proceedings of the Edinburgh Mathematical Society",

issn = "0013-0915",

publisher = "Cambridge University Press",

number = "1",

}

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 -