Weighted $H^p$ spaces

José García-Cuerva

GDML_Books, (1979), p.

Résumé

CONTENTSIntroduction.......................................................................................................................................................... 5Chapter I. Some preliminary lemmas............................................................................................................ 8Chapter II. Weighted $H^p$ spaces of analytic functions.......................................................................... 13 1. Behaviour at the boundary....................................................................................................................... 13 2. Maximal function characterization........................................................................................................... 15 3. Atomic decomposition.............................................................................................................................. 20 4. Dual spaces............................................................................................................................................... 27Chapter III. $H^p$ spaces associated with the space of homogeneous type (R, w(x)dx).................... 31 1. The space $\mathfrak {H}^1(w(x)dx)$...................................................................................................... 31 2. The spaces $\mathfrak {H}^p(w(x)dx)$ for p < 1.................................................................................... 33Chapter IV. Applications and examples.......................................................................................................... 40 1. A weighted Hilbert transform.................................................................................................................... 40 2. Equivalence between the space of radial functions in $H^1(R^n)$ and the space of even functions in $\mathfrak {H}^1(|r|^{n-1}dr)$..................................................................................... 40 3. Integral operators in the line obtained by restricting to radial functions some systems of Riesz transforms in higher dimensions................................................................................................. 44 4. The kernel $z^{-2}$...................................................................................................................................... 54References............................................................................................................................................................. 58

Détail

EUDML-ID : urn:eudml:doc:268606