Wavelet characterization and modular inequalities for weighted Lebesgue spaces with variable exponent

Continuous wavelet transform in variable Lebesgue spaces

In the present note we investigate norm and almost everywhere convergence of the inverse continuous wavelet transform in the variable Lebesgue space. Mathematics Subject Classification (2010): Primary 42C40, Secondary 42C15, 42B08, 42A38, 46B15.

Some functional inequalities in variable exponent spaces with a more generalization of uniform continuity condition

‎Some functional inequalities‎ ‎in variable exponent Lebesgue spaces are presented‎. ‎The bi-weighted modular inequality with variable exponent $p(.)$ for the Hardy operator restricted to non‎- ‎increasing function which is‎‎$$‎‎int_0^infty (frac{1}{x}int_0^x f(t)dt)^{p(x)}v(x)dxleq‎‎Cint_0^infty f(x)^{p(x)}u(x)dx‎,‎$$‎ ‎is studied‎. ‎We show that the exponent $p(.)$ for which these modular ine...

On The Sobolev-type Inequality for Lebesgue Spaces with a Variable Exponent

The Wavelet Characterization of Herz-type Hardy Spaces with Variable Exponent

In this paper, using the atomic theory of the Herz-type Hardy spaces with variable exponent, we give their wavelet characterization by means of some discrete tent spaces with variable exponent at the origin.

Vector-valued Inequalities on Herz Spaces and Characterizations of Herz–sobolev Spaces with Variable Exponent

The origin of Herz spaces is the study of characterization of functions and multipliers on the classical Hardy spaces ([1, 8]). By virtue of many authors’ works Herz spaces have became one of the remarkable classes of function spaces in harmonic analysis now. One of the important problems on the spaces is boundedness of sublinear operators satisfying proper conditions. Hernández, Li, Lu and Yan...