Compact composition operators on weighted Hilbert spaces of analytic functions

Abstract

We characterize the compactness of composition operators; in term of generalized Nevanlinna counting functions, on a large class of Hilbert spaces of analytic functions, which can be viewed between the Bergman and the Dirichlet spaces1

Essential norm of composition operators between weighted Hardy spaces

“…H w 2 . The boundedness of the operator is characterized first, which slightly extends Theorem 1.3 in [15]. In the main result of this paper an asymptotic formula for the essential norm of the operator is given which considerably extends the main result in [15].…”

“…Such a weight function is called admissible ( [15]). If w satisfies conditions: ðW 1 Þ; ðW 2 Þ; ðW 3 Þ and ðW 4 Þ, then it is said that w is (I)-admissible.…”

“…[2,[6][7][8][9][10][11][12][13][14][15][16][17][18][20][21][22]25,[28][29][30][31][32][33][34][35]). …”

“…Let w 1 and w 2 be two admissible weight functions. Motivated by [15], in this paper we study the composition operator C u : H w 1 ! H w 2 .…”

Generalized Composition Operators on Weighted Hilbert Spaces of Analytic Functions

“…We refer the reader to the monographs ( [6], [8], [9], [23], [29], [30]), the papers ( [3]- [5]) and the references therein for the overview of the field as of the early 1990s. Composition operators on the weighted Hilbert space H ω have been studied by many authors, see for example [11], [22] and the related references therein.…”