On generalized Lorentz-Zygmund spaces

Multiplication Operators on Generalized Lorentz-zygmund Spaces

The invertible, compact and Fredholm multiplication operators on generalized Lorentz-Zygmund (GLZ) spaces Lp,q;α, 1 < p ≤ ∞, 1 ≤ q ≤ ∞, α in the Euclidean space R, are characterized in this paper.

Are Generalized Lorentz “spaces” Really Spaces?

We show that the Lorentz space Λp(w) need not be a linear set for certain “non-classical” weights w. We establish necessary and sufficient conditions on p and w for this situation to occur.

Generalized Composition Operators from Zygmund Type Spaces to Qk Spaces

Let φ be an analytic self-map of D and g∈H(D) . The boundedness and compactness of generalized composition operators

Volterra-Type Operators on Zygmund Spaces

On an Optimal Decomposition in Zygmund Spaces

An optimal decomposition formula for the norm in the Orlicz space L(log L) is given. New proofs of some results involving L(log L) spaces are given and the decomposition is applied to apriori estimates for elliptic partial differential equations with the right-hand side in Zygmund classes. 2000 Mathematics Subject Classification: 46E35, 46E39, 35J05.