VECTOR MEASURES OF BOUNDED SEMIVARIATION AND ASSOCIATED CONVOLUTION OPERATORS
Glasgow mathematical journal, Tome 53 (2011) no. 2, pp. 333-340
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Let G be a compact metrizable abelian group, and let X be a Banach space. We characterize convolution operators associated with a regular Borel X-valued measure of bounded semivariation that are compact (resp; weakly compact) from L1(G), the space of integrable functions on G into L1(G) X, the injective tensor product of L1(G) and X. Along the way we prove a Fourier Convergence theorem for vector measures of relatively compact range that are absolutely continuous with respect to the Haar measure.
SAAB, PAULETTE; ROBDERA, MANGATIANA A. VECTOR MEASURES OF BOUNDED SEMIVARIATION AND ASSOCIATED CONVOLUTION OPERATORS. Glasgow mathematical journal, Tome 53 (2011) no. 2, pp. 333-340. doi: 10.1017/S0017089510000741
@article{10_1017_S0017089510000741,
author = {SAAB, PAULETTE and ROBDERA, MANGATIANA A.},
title = {VECTOR {MEASURES} {OF} {BOUNDED} {SEMIVARIATION} {AND} {ASSOCIATED} {CONVOLUTION} {OPERATORS}},
journal = {Glasgow mathematical journal},
pages = {333--340},
year = {2011},
volume = {53},
number = {2},
doi = {10.1017/S0017089510000741},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000741/}
}
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%0 Journal Article %A SAAB, PAULETTE %A ROBDERA, MANGATIANA A. %T VECTOR MEASURES OF BOUNDED SEMIVARIATION AND ASSOCIATED CONVOLUTION OPERATORS %J Glasgow mathematical journal %D 2011 %P 333-340 %V 53 %N 2 %U http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000741/ %R 10.1017/S0017089510000741 %F 10_1017_S0017089510000741
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