Discretization and Transference of Bisublinear Maximal Operators |
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Authors: | Earl Berkson Oscar Blasco María J Carro TA Gillespie |
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Institution: | (1) Department of Mathematics, University of Illinois, 1409 W. Green St., Urbana, IL 61801, USA;(2) Departamento de Análisis Matemático, Universidad de Valencia, 46100 (Burjassot), Valencia, Spain;(3) Dept. App. Math. and Analysis, Universitat de Barcelona, Gran Via 585, 08071, Barcelona, Spain;(4) Department of Mathematics and Statistics, University of Edinburgh, James Clerk Maxwell Building, Edinburgh EH9 3JZ, Scotland, UK |
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Abstract: | We develop a general condition for automatically discretizing strong type bisublinear maximal estimates that arise in the
context of the real line. In particular, this method applies directly to Michael Lacey’s strong type boundedness results for
the bisublinear maximal Hilbert transform and for the bisublinear Hardy-Littlewood maximal operator, furnishing the counterpart
of each of these two results (without changes to the range of exponents) for the sequence spaces
We then take up some transference applications of discretized maximal bisublinear operators to maximal estimates and almost
everywhere convergence in Lebesgue spaces of abstract measures. We also broaden the scope of such applications, which are
based on transference from
by developing general methods for transplanting bisublinear maximal estimates from arbitrary locally compact abelian groups. |
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Keywords: | |
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