In the present paper, the ne spectrum of the Zweier matrix as anoperator over the weighted sequence space `p(w); have been examined.

Let ϕ be a holomorphic self-map and let ψ be a holomorphic function on the unit ball B. The boundedness and compactness of the weighted composition operator ψC ϕ from the generalized weighted Bergman space into a class of weighted-type spaces are studied in this paper.

In this paper, we characterize those holomorphic symbols u on the unit ball B and holomorphic self-mappings φ of B for which the weighted composition operator uCφ is bounded or compact from Bloch-type space to H∞ space. Mathematics subject classification (2010): Primary 47B33; Secondary 47B38.

‎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...