Estimates for vector-valued holomorphic functions and Littlewood-Paley-Stein theory

Mark Veraar, and Lutz Weis. "Estimates for vector-valued holomorphic functions and Littlewood-Paley-Stein theory." Studia Mathematica 228.1 (2015): 73-99. <http://eudml.org/doc/285377>.

@article{MarkVeraar2015,
abstract = {We consider generalized square function norms of holomorphic functions with values in a Banach space. One of the main results is a characterization of embeddings of the form $L^\{p\}(X) ⊆ γ(X) ⊆ L^\{q\}(X)$, in terms of the type p and cotype q of the Banach space X. As an application we prove $L^\{p\}$-estimates for vector-valued Littlewood-Paley-Stein g-functions and derive an embedding result for real and complex interpolation spaces under type and cotype conditions.},
author = {Mark Veraar, Lutz Weis},
journal = {Studia Mathematica},
keywords = {vector-valued holomorphic functions; type; cotype; Littlewood-Paley -function; Fourier type; embedding; real interpolation; complex interpolation; functional calculus},
language = {eng},
number = {1},
pages = {73-99},
title = {Estimates for vector-valued holomorphic functions and Littlewood-Paley-Stein theory},
url = {http://eudml.org/doc/285377},
volume = {228},
year = {2015},
}

TY - JOUR
AU - Mark Veraar
AU - Lutz Weis
TI - Estimates for vector-valued holomorphic functions and Littlewood-Paley-Stein theory
JO - Studia Mathematica
PY - 2015
VL - 228
IS - 1
SP - 73
EP - 99
AB - We consider generalized square function norms of holomorphic functions with values in a Banach space. One of the main results is a characterization of embeddings of the form $L^{p}(X) ⊆ γ(X) ⊆ L^{q}(X)$, in terms of the type p and cotype q of the Banach space X. As an application we prove $L^{p}$-estimates for vector-valued Littlewood-Paley-Stein g-functions and derive an embedding result for real and complex interpolation spaces under type and cotype conditions.
LA - eng
KW - vector-valued holomorphic functions; type; cotype; Littlewood-Paley -function; Fourier type; embedding; real interpolation; complex interpolation; functional calculus
UR - http://eudml.org/doc/285377
ER -