Embedding Theorems for Dirichlet Type Spaces

Abstract

Using Carleson measure theorem of weighted Bergman spaces, we provide a complete characterization of embedding theorem for Dirichlet type spaces. As an application, we study the Volterra integral operator and multipliers for Dirichlet type spaces.2000 Mathematics Subject Classification. 30H30, 47B38.

Volterra integral operators and Carleson embedding on Campanato spaces

“…Pau and Peláez [18] and Xiao [10] studied T g acting on Q p , respectively. For more information on operator T g , see [3,8,11,14,16,17,19,20,21,22,23,24] and the references therein.…”

Embedding of Besov Spaces and the Volterra Integral Operator

“…Recently, the operator T g has been receiving much attention. See [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] and the references therein for more study of the operator T g .…”

“…is bounded if and only if μ is a p-logarithmic s-Carleson measure. In [9], Li et al proved that the inclusion mapping…”

Dirichlet-Morrey type spaces and Volterra integral operators

“…The Volterra integral operator T g was studied by many authors recently. For more results on operator T g , we refer to [5,7,8,9,10,11,12,13,14,15,16,17,18,19] and the references therein For any I ⊂ ∂ D, the boundary of D, let |I| be the normalized arc length of I. Let…”