Function Spaces and Their Operators
A Conference in Honor of Richard Rochberg on the Occasion
of his 65th Birthday
Marcin Bownik from the University of Oregon; Duality and interpolation of anisotropic Triebel-Lizorkin spaces; May 31, 2008.
Abstract: In this talk we introduce anisotropic Triebel-Lizorkin spaces associated
with general expansive dilations and doubling measures on $R^n$ using
wavelet transforms. To achieve this we generalize the isotropic methods of
dyadic $\varphi$-transforms of Frazier and Jawerth to non-isotropic
settings.
By working at the level of sequence spaces, we identify the duals of
anisotropic Triebel-Lizorkin spaces. We also obtain several real and complex
interpolation results for these spaces.