UMD spaces

2016 ◽  
pp. 267-372
Author(s):  
Tuomas Hytönen ◽  
Jan van Neerven ◽  
Mark Veraar ◽  
Lutz Weis
Keyword(s):  
Umd Spaces

scholarly journals THE LOCAL NON-HOMOGENEOUS Tb THEOREM FOR VECTOR-VALUED FUNCTIONS

2014 ◽  
Vol 57 (1) ◽  
pp. 17-82 ◽  
Author(s):  
TUOMAS P. HYTÖNEN ◽  
ANTTI V. VÄHÄKANGAS
Keyword(s):  
Singular Integrals ◽  
Local Version ◽  
Square Functions ◽  
Property A ◽  
Martingale Differences ◽  
Umd Spaces ◽  
Function Lattice ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Similar Extension

AbstractWe extend the local non-homogeneous Tb theorem of Nazarov, Treil and Volberg to the setting of singular integrals with operator-valued kernel that act on vector-valued functions. Here, ‘vector-valued’ means ‘taking values in a function lattice with the UMD (unconditional martingale differences) property’. A similar extension (but for general UMD spaces rather than UMD lattices) of Nazarov-Treil-Volberg's global non-homogeneous Tb theorem was achieved earlier by the first author, and it has found applications in the work of Mayboroda and Volberg on square-functions and rectifiability. Our local version requires several elaborations of the previous techniques, and raises new questions about the limits of the vector-valued theory.

scholarly journals Square functions in the Hermite setting for functions with values in UMD spaces

2013 ◽  
Vol 193 (5) ◽  
pp. 1397-1430 ◽  
Author(s):  
J. J. Betancor ◽  
A. J. Castro ◽  
J. Curbelo ◽  
J. C. Fariña ◽  
L. Rodríguez-Mesa
Keyword(s):  
Square Functions ◽  
Umd Spaces

scholarly journals Some remarks on complex powers of $(-\Delta)$ and UMD spaces

1991 ◽  
Vol 35 (3) ◽  
pp. 401-407 ◽  
Author(s):  
Sylvie Guerre-Delabriere
Keyword(s):  
Umd Spaces ◽  
Complex Powers

scholarly journals A Simplified Approach in the Study of Elliptic Differential Equations in UMD Spaces and New Applications

2008 ◽  
Vol 51 (2) ◽  
pp. 165-187 ◽  
Author(s):  
Angelo Favini ◽  
Rabah Labbas ◽  
Stéphane Maingot ◽  
Hiroki Tanabe ◽  
Atsushi Yagi
Keyword(s):  
Differential Equations ◽  
Simplified Approach ◽  
Umd Spaces ◽  
Elliptic Differential Equations ◽  
New Applications

scholarly journals Wavelet transform for functions with values in UMD spaces

2008 ◽  
Vol 186 (2) ◽  
pp. 101-126 ◽  
Author(s):  
Cornelia Kaiser ◽  
Lutz Weis
Keyword(s):  
Wavelet Transform ◽  
Umd Spaces

On the inverse Laplace transform for C 0 -semigroups in UMD-spaces

1999 ◽  
Vol 72 (1) ◽  
pp. 56-63 ◽  
Author(s):  
A. Driouich ◽  
O. El-Mennaoui
Keyword(s):  
Laplace Transform ◽  
Inverse Laplace Transform ◽  
Umd Spaces

scholarly journals A note on UMD spaces and transference in vector-valued function spaces

1996 ◽  
Vol 39 (3) ◽  
pp. 485-490 ◽  
Author(s):  
N. H. Asmar ◽  
B. P. Kelly ◽  
S. Montgomery-Smith
Keyword(s):  
Banach Space ◽  
Hilbert Transform ◽  
Function Spaces ◽  
Conjugate Functions ◽  
Riesz Theorem ◽  
Umd Spaces ◽  
The Hilbert Transform ◽  
Vector Valued Function ◽  
Vector Valued

A Banach space X is called an HT space if the Hilbert transform is bounded from Lp(X) into Lp(X), where 1 < p < ∞. We introduce the notion of an ACF Banach space, that is, a Banach space X for which we have an abstract M. Riesz Theorem for conjugate functions in Lp(X), 1 < p < ∞. Berkson, Gillespie and Muhly [5] showed that X ∈ HT ⇒ X ∈ ACF. In this note, we will show that X ∈ ACF ⇒ X ∈ UMD, thus providing a new proof of Bourgain's result X ∈ HT ⇒ X ∈ UMD.

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