Multipliers and integration operators on Dirichlet spaces

Abstract

Abstract. For 0 < p < ∞ and α > −1, we let D p α denote the space of those functions f which are analytic in the unit disc D in C and satisfy

Embedding theorems and integration operators on Bergman spaces with rapidly decreasing weights

“…where g is an analytic function on D. The boundedness and compactness of T g on classical spaces has attracted a lot of attention in recent years (see [2,3] for Hardy spaces, [4,10,25] for weighted Bergman spaces, and [13,14] for Dirichlet-type spaces). We also mention the surveys [1] and [27] for an account of results and open questions on the operator T g .…”

The spectrum of Volterra-type integration operators on generalized Fock spaces

“…There is an extensive literature regarding the boundedness, compactness, and Schatten class membership of T g on various spaces of analytic functions (see [2,6] for Hardy spaces, [3,5,9,15,18,16] for weighted Bergman spaces, [12,13] for Dirichlet spaces, [10,11] for Fock spaces, [7,8] for growth spaces of entire functions, as well as the surveys [1,19] and references therein). One of the key tools in all these considerations is a Littlewood-Paleytype estimate for the target space of the operator, which, for a wide class of radial weights, can be obtained by standard techniques.…”

Boundary multipliers of a family of Möbius invariant function spaces

“…A characterization of the pointwise multipliers M(Q s (D)) was obtained in [18] proving a conjecture stated in [28]. See [10,17,22,25,27,35] for more results on pointwise multipliers of function spaces.…”