STABILITY OF LOCALIZED INTEGRAL OPERATORS ON WEIGHTED L-p SPACES

    Authors

    K. S. Rim; C. E. Shin;Q. Y. Sun

    Comments

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    Abbreviated Journal Title

    Numer. Funct. Anal. Optim.

    Keywords

    Bessel potential; Bootstrap technique; Doubling measure; Infinite; matrix; Integral operator; Muckenhoupt weight; Reverse Holder; inequality; Spectrum; Wiener's lemma; Weighted function space; BANACH ALGEBRA; WIENERS LEMMA; SPECTRUM; Mathematics, Applied

    Abstract

    In this article, we consider localized integral operators whose kernels have mild singularity near the diagonal and certain Holder regularity and decay off the diagonal. Our model example is the Bessel potential operator J(gamma), gamma > 0. We show that if such a localized integral operator has stability on a weighted function space L-w(p) for some p epsilon [1,infinity) and Muckenhoupt A(p)-weight w, then it has stability on weighted function spaces L-w'(p') and Muckenhoupt A(p')-weights w' for all p' epsilon [1,infinity).

    Journal Title

    Numerical Functional Analysis and Optimization

    Volume

    33

    Issue/Number

    7-9

    Publication Date

    1-1-2012

    Document Type

    Article

    Language

    English

    First Page

    1166

    Last Page

    1193

    WOS Identifier

    WOS:000307080400021

    ISSN

    0163-0563

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