Weighted $H^p$ spaces

José García-Cuerva. Weighted $H^p$ spaces. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1979. <http://eudml.org/doc/268606>.

@book{JoséGarcía1979,
abstract = {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},
author = {José García-Cuerva},
keywords = {maximal function; building blocks; homogeneous space},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Weighted $H^p$ spaces},
url = {http://eudml.org/doc/268606},
year = {1979},
}

TY - BOOK
AU - José García-Cuerva
TI - Weighted $H^p$ spaces
PY - 1979
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - 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
LA - eng
KW - maximal function; building blocks; homogeneous space
UR - http://eudml.org/doc/268606
ER -