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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:384

Article

Karlovich, Alexei Yu¹  Spitkovsky, Ilya M.² 

[1] Univ Nova Lisboa, Fac Ciencias & Tecnol, Dept Matemat, P-2829516 Quinta Da Torre, Caparica, Portugal

[2] Coll William & Mary, Dept Math, Williamsburg, VA 23187 USA

关键词: Almost-periodic function;    Semi-almost periodic function;    Slowly oscillating function;    Variable Lebesgue space;    Singular integral operator;    Fredholmness;    Invertibility;   

DOI  :  10.1016/j.jmaa.2011.06.066

来源: Elsevier

【 摘 要 】

Let a be a semi-almost periodic matrix function with the almost periodic representatives a(l) and a(r) at infinity and +infinity, respectively. Suppose p : R -> (1, infinity) is a slowly oscillating exponent such that the Cauchy singular integral operator S is bounded on the variable Lebesgue space L-p(.)(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 L-N(p(.))(R), then the operators a(l)P + Q and a(r)P + Q are invertible on standard Lebesgue spaces L-N(ql)(R) and L-N(qr)(R) with some exponents q(l) and q(r) lying in the segments between the lower and the upper limits of p at -infinity and +infinity, respectively. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free