Poincaré-type Inequality for Variable Exponent Spaces of Differential Forms

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

On modular inequalities in variable Lpspaces

We show that the Hardy-Littlewood maximal operator and a class of CalderónZygmund singular integrals satisfy the strong type modular inequality in variable Lp spaces if and only if the variable exponent p(x) ∼ const.

A Sobolev Poincaré Type Inequality for Integral Varifolds

In this work a local inequality is provided which bounds the distance of an integral varifold from a multivalued plane (height) by its tilt and mean curvature. The bounds obtained for the exponents of the Lebesgue spaces involved are shown to be sharp.

m at h . C A ] 1 2 M ay 2 00 4 ON MODULAR INEQUALITIES IN VARIABLE L p SPACES

We show that the Hardy-Littlewood maximal operator and a class of Calderón-Zygmund singular integrals satisfy the strong type modular inequality in variable L spaces if and only if the variable exponent p(x) ∼ const.