A regularity principle in sequence spaces and applications

Computer Assisted Fourier Analysis in Sequence Spaces of Varying Regularity

This work treats a functional analytic framework for computer assisted Fourier analysis which can be used to obtain mathematically rigorous error bounds on numerical approximations of solutions of differential equations. An abstract a-posteriori theorem is employed in order to obtain existence and regularity results for C problems with 0 < k ≤ ∞ or k = ω. The main tools are certain infinite seq...

A New Class of Banach Sequence Spaces

Concentration-compactness Principle for Variable Exponent Spaces and Applications

In this article, we extend the well-known concentration compactness principle by Lions to the variable exponent case. We also give some applications to the existence problem for the p(x)-Laplacian with critical growth.

The Concentration-compactness Principle for Variable Exponent Spaces and Applications

In this paper we extend the well-known concentration – compactness principle of P.L. Lions to the variable exponent case. We also give some applications to the existence problem for the p(x)−Laplacian with critical growth.

Arens regularity of bilinear forms and unital Banach module spaces

Assume that $A$‎, ‎$B$ are Banach algebras and that $m:Atimes Brightarrow B$‎, ‎$m^prime:Atimes Arightarrow B$ are bounded bilinear mappings‎. ‎We study the relationships between Arens regularity of $m$‎, ‎$m^prime$ and the Banach algebras $A$‎, ‎$B$‎. ‎For a Banach $A‎$‎-bimodule $B$‎, ‎we show that $B$ factors with respect to $A$ if and only if $B^{**}$ is unital as an $A^{**}‎$‎-module‎. ‎Le...