On singular integral operators with semi-almost periodic coefficients on variable Lebesgue spaces

Alexei Yu Karlovich, Ilya Spitkovsky

    Research output: Contribution to journalArticle

    Abstract

    Let a be a semi-almost periodic matrix function with the almost periodic representatives al and ar at -∞ and +∞, respectively. Suppose p:R→(1,∞) is a slowly oscillating exponent such that the Cauchy singular integral operator S is bounded on the variable Lebesgue space Lp(.)(R). We prove that if the operator aP+Q with P=(I+S)/2 and Q=(I-S)/2 is Fredholm on the variable Lebesgue space LNp(.)(R), then the operators alP+Q and arP+Q are invertible on standard Lebesgue spaces LNql(R) and LNqr(R) with some exponents ql and qr lying in the segments between the lower and the upper limits of p at -∞ and +∞, respectively.

    Original languageEnglish (US)
    Pages (from-to)706-725
    Number of pages20
    JournalJournal of Mathematical Analysis and Applications
    Volume384
    Issue number2
    DOIs
    StatePublished - Dec 15 2011

    Fingerprint

    Singular Integral Operator
    Periodic Coefficients
    Lebesgue Space
    Almost Periodic
    Si
    Exponent
    Cauchy Integral
    Matrix Function
    Operator
    Periodic Functions
    Invertible

    Keywords

    • Almost-periodic function
    • Fredholmness
    • Invertibility
    • Semi-almost periodic function
    • Singular integral operator
    • Slowly oscillating function
    • Variable Lebesgue space

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

    Cite this

    On singular integral operators with semi-almost periodic coefficients on variable Lebesgue spaces. / Karlovich, Alexei Yu; Spitkovsky, Ilya.

    In: Journal of Mathematical Analysis and Applications, Vol. 384, No. 2, 15.12.2011, p. 706-725.

    Research output: Contribution to journalArticle

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