scholarly journals Atomic Hardy space theory for unbounded singular integrals

2006 ◽  
Vol 55 (4) ◽  
pp. 1461-1482
Author(s):  
Ryan Berndt
Keyword(s):  
Hardy Space ◽  
Singular Integrals ◽  
Space Theory ◽  
Atomic Hardy Space

SINGULAR INTEGRALS SUPPORTED BY SUBVARIETIES FOR VECTOR-VALUED FUNCTIONS

2017 ◽  
Vol 231 ◽  
pp. 101-114
Author(s):  
HONGHAI LIU
Keyword(s):  
Singular Integrals ◽  
Operator Space ◽  
Space Theory ◽  
Umd Space ◽  
Vector Valued Functions ◽  
Vector Valued

In this paper, we show that singular integrals supported by subvarieties are bounded on $L^{p}(\mathbb{R}^{n};\mathbf{X})$ for $1<p<\infty$ and some UMD space $\mathbf{X}$. In the terminology from operator space theory, we prove that singular integrals supported by subvarieties are completely $L^{p}$-bounded.

scholarly journals Product Space Singular Integrals with Mild Kernel Regularity

2021 ◽  
Vol 32 (1) ◽  
Author(s):  
Emil Airta ◽  
Henri Martikainen ◽  
Emil Vuorinen
Keyword(s):  
Product Space ◽  
Singular Integrals ◽  
Structural Theory ◽  
Space Theory

AbstractWe develop product space theory of singular integrals with mild kernel regularity. We study these kernel regularity questions specifically in situations that are very tied to the T1 type arguments and the corresponding structural theory. In addition, our results are multilinear.

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

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
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