Weighted kernel operators in variable exponent amalgam spaces

Abstract

The paper is devoted to weighted inequalities for positive kernel operators in variable exponent amalgam spaces. In particular, a characterization of a weight v governing the boundedness/compactness of the weighted kernel operators [InlineEquation not available: see fulltext.] and [InlineEquation not available: see fulltext.], defined on [InlineEquation not available: see fulltext.] and ℝ, respectively, under the log-Hölder continuity condition on exponents of spaces is established. These operators involve, for example, weighted variable parameter fractional integrals. The results are new even for constant exponent amalgam spaces. MSC: 46E30, 47B34. © 2013 Kokilashvili et al.; licensee Springer.