Lipschitz Continuous and Compact Composition Operator Acting Between Some Weighted General Hyperbolic-Type Classes

Abstract

Abstract. In this paper, we study Lipschitz continuous, the boundedness and compactness of the composition operator C φ acting between the general hyperbolic Bloch type-classes B * p,log,α and general hyperbolic Besov-type classes F * p,log (p, q, s). Moreover, these classes are shown to be complete metric spaces with respect to the corresponding metrics.

Certain Classes of Operators on Some Weighted Hyperbolic Function Spaces

“…Dealing with corresponding concerned spaces of weighted functions on the disk Δ, essential properties of the new type of operators are discussed. ere are some certain attempts to study hyperbolic function spaces (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and others). Most research studies were on composition operators.…”