scholarly journals On bounded functions in the abstract Hardy space theory, II

1974 ◽  
Vol 26 (4) ◽  
pp. 513-533 ◽  
Author(s):  
Kôzô Yabuta
Keyword(s):  
Hardy Space ◽  
Space Theory ◽  
Bounded Functions ◽  
Abstract Hardy Space

M. Riesz's theorem in the abstract Hardy space theory

1977 ◽  
Vol 29 (1) ◽  
pp. 308-312 ◽  
Author(s):  
K�z� Yabuta
Keyword(s):  
Hardy Space ◽  
Space Theory ◽  
Abstract Hardy Space

scholarly journals THE JOINT SIMILARITY PROBLEM FOR WEIGHTED BERGMAN SHIFTS

2002 ◽  
Vol 45 (1) ◽  
pp. 117-139 ◽  
Author(s):  
Sarah H. Ferguson ◽  
Srdjan Petrovic
Keyword(s):  
Hardy Space ◽  
Primary 47B35 ◽  
Bergman Spaces ◽  
Subject Classification ◽  
Weighted Bergman Spaces ◽  
Space Theory ◽  
Single Operator ◽  
Similarity Problem

AbstractWe solve a joint similarity problem for pairs of operators of Foias–Williams/Peller type on weighted Bergman spaces. We show that for the single operator, the Hardy space theory established by Bourgain and Aleksandrov–Peller carries over to weighted Bergman spaces, by establishing the relevant weak factorizations. We then use this fact, together with a recent dilation result due to the first author and Rochberg, to show that a commuting pair of such operators is jointly polynomially bounded if and only if it is jointly completely polynomially bounded. In this case, the pair is jointly similar to a pair of contractions by Paulsen’s similarity theorem.AMS 2000 Mathematics subject classification: Primary 47B35; 47B47

scholarly journals HARDY SPACES ON METRIC MEASURE SPACES WITH GENERALIZED SUB-GAUSSIAN HEAT KERNEL ESTIMATES

2017 ◽  
Vol 104 (2) ◽  
pp. 162-194
Author(s):  
LI CHEN
Keyword(s):  
Hardy Space ◽  
Heat Kernel ◽  
Hardy Spaces ◽  
Riesz Transform ◽  
Square Function ◽  
Space Theory ◽  
Metric Measure Spaces ◽  
Kernel Estimates ◽  
Previous Theory ◽  
Measure Spaces

Hardy space theory has been studied on manifolds or metric measure spaces equipped with either Gaussian or sub-Gaussian heat kernel behaviour. However, there are natural examples where one finds a mix of both behaviours (locally Gaussian and at infinity sub-Gaussian), in which case the previous theory does not apply. Still we define molecular and square function Hardy spaces using appropriate scaling, and we show that they agree with Lebesgue spaces in some range. Besides, counterexamples are given in this setting that the $H^{p}$ space corresponding to Gaussian estimates may not coincide with $L^{p}$. As a motivation for this theory, we show that the Riesz transform maps our Hardy space $H^{1}$ into $L^{1}$.

Sign in / Sign up

Export Citation Format

Share Document