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Maximal functions for groups of operators.

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Maximal functions for groups of operators. / Blower, Gordon.
In: Proceedings of the Edinburgh Mathematical Society, Vol. 43, No. 1, 02.2000, p. 57-71.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Blower, G 2000, 'Maximal functions for groups of operators.', Proceedings of the Edinburgh Mathematical Society, vol. 43, no. 1, pp. 57-71. https://doi.org/10.1017/S0013091500020691

APA

Blower, G. (2000). Maximal functions for groups of operators. Proceedings of the Edinburgh Mathematical Society, 43(1), 57-71. https://doi.org/10.1017/S0013091500020691

Vancouver

Blower G. Maximal functions for groups of operators. Proceedings of the Edinburgh Mathematical Society. 2000 Feb;43(1):57-71. doi: 10.1017/S0013091500020691

Author

Blower, Gordon. / Maximal functions for groups of operators. In: Proceedings of the Edinburgh Mathematical Society. 2000 ; Vol. 43, No. 1. pp. 57-71.

Bibtex

@article{173efc4912294d088cf09fa6f15c0d4a,
title = "Maximal functions for groups of operators.",
abstract = "Let Δ be the Laplace operator on d and 1 < δ < 2. Using transference methods we show that, for max {q, q/(q – 1)} < 4d/(2d + 1 – δ), the maximal function for the Schr{\"o}dinger group is in Lq, for f Lq with Δδ/2 f Lq. We obtain a similar result for the Airy group exp it Δ3/2. An abstract version of these results is obtained for bounded C0-groups eitL on subspaces of Lp spaces. Certain results extend to maximal functions defined for functions with values in U M D Banach spaces.",
author = "Gordon Blower",
note = "http://journals.cambridge.org/action/displayJournal?jid=PEM The final, definitive version of this article has been published in the Journal, Proceedings of the Edinburgh Mathematical Society, 43 (1), pp 57-71 2000, {\textcopyright} 2000 Cambridge University Press.",
year = "2000",
month = feb,
doi = "10.1017/S0013091500020691",
language = "English",
volume = "43",
pages = "57--71",
journal = "Proceedings of the Edinburgh Mathematical Society",
issn = "0013-0915",
publisher = "Cambridge University Press",
number = "1",

}

RIS

TY - JOUR

T1 - Maximal functions for groups of operators.

AU - Blower, Gordon

N1 - http://journals.cambridge.org/action/displayJournal?jid=PEM The final, definitive version of this article has been published in the Journal, Proceedings of the Edinburgh Mathematical Society, 43 (1), pp 57-71 2000, © 2000 Cambridge University Press.

PY - 2000/2

Y1 - 2000/2

N2 - Let Δ be the Laplace operator on d and 1 < δ < 2. Using transference methods we show that, for max {q, q/(q – 1)} < 4d/(2d + 1 – δ), the maximal function for the Schrödinger group is in Lq, for f Lq with Δδ/2 f Lq. We obtain a similar result for the Airy group exp it Δ3/2. An abstract version of these results is obtained for bounded C0-groups eitL on subspaces of Lp spaces. Certain results extend to maximal functions defined for functions with values in U M D Banach spaces.

AB - Let Δ be the Laplace operator on d and 1 < δ < 2. Using transference methods we show that, for max {q, q/(q – 1)} < 4d/(2d + 1 – δ), the maximal function for the Schrödinger group is in Lq, for f Lq with Δδ/2 f Lq. We obtain a similar result for the Airy group exp it Δ3/2. An abstract version of these results is obtained for bounded C0-groups eitL on subspaces of Lp spaces. Certain results extend to maximal functions defined for functions with values in U M D Banach spaces.

U2 - 10.1017/S0013091500020691

DO - 10.1017/S0013091500020691

M3 - Journal article

VL - 43

SP - 57

EP - 71

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

SN - 0013-0915

IS - 1

ER -