‎by considering a degenerate $p(x)-$laplacian equation‎, ‎a generalized compact embedding in weighted variable‎ ‎exponent sobolev space is presented‎. ‎multiplicity of positive solutions are discussed by applying fibering map approach for the‎ ‎corresponding nehari manifold‎.

The common topic of this thesis is boundedness of integral and supremal operators between function spaces with weights. The results of this work have the form of characterizations of validity of weighted operator inequalities for appropriate cones of functions. The outcome can be divided into three categories according to the particular type of studied operators and function spaces. The first p...

We study the strong continuity of weighted composition semigroups of the form Ttf = φ′t (f ◦ φt) in several spaces of analytic functions. First we give a general result on separable spaces and use it to prove that these semigroups are always strongly continuous in the Hardy and Bergman spaces. Then we focus on two non-separable family of spaces, the mixed norm and the weighted Banach spaces. We...

We consider Banach spaces of analytic functions in the unit disc which satisfy a weighted conformal invariance property, that is, for fixed ?>0 and every automorphism ? disc, f?f??(??)? defines bounded linear operator on space question, family all such operators is uniformly norm. Many common examples like Korenblum growth classes, Hardy spaces, standard Bergman certain Besov this condition. Th...

We prove the null controllability of a one-dimensional degenerate parabolic equation with drift and singular potential. study case when potential arises at left endpoint weighted Dirichlet boundary control is located this point. get spectral decomposition suitable operator, defined in Sobolev space, involving Bessel functions their zeros, then we use moment method by Fattorini Russell to obtain...