# Positive kernel operators in $$L^{p(x)}$$ spaces

Positive kernel operators in $$L^{p(x)}$$ spaces A characterization of a weight $$v$$ governing the boundedness/compactness of the weighted kernel operator $$K_v$$ in variable exponent Lebesgue spaces $$L^{p(\cdot )}$$ is established under the log-Hölder continuity condition on exponents of spaces. The kernel operator involves, for example, weighted variable parameter fractional integral operators. The distance between $$K_v$$ and the class of compact integral operators acting from $$L^{p(\cdot )}$$ to $$L^{q(\cdot )}$$ (measure of non-compactness) is also estimated from above and below. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# Positive kernel operators in $$L^{p(x)}$$ spaces

, Volume 17 (4) – Feb 3, 2013
18 pages

/lp/springer_journal/positive-kernel-operators-in-l-p-x-spaces-gSkdS03GNf
Publisher
Springer Basel
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-013-0225-9
Publisher site
See Article on Publisher Site

### Abstract

A characterization of a weight $$v$$ governing the boundedness/compactness of the weighted kernel operator $$K_v$$ in variable exponent Lebesgue spaces $$L^{p(\cdot )}$$ is established under the log-Hölder continuity condition on exponents of spaces. The kernel operator involves, for example, weighted variable parameter fractional integral operators. The distance between $$K_v$$ and the class of compact integral operators acting from $$L^{p(\cdot )}$$ to $$L^{q(\cdot )}$$ (measure of non-compactness) is also estimated from above and below.

### Journal

PositivitySpringer Journals

Published: Feb 3, 2013

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