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 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

Complex powers of eta-function

2018 ◽  
Vol 14 (06) ◽  
pp. 1619-1625
Author(s):  
Alexander Zuevsky
Keyword(s):  
Riemann Surface ◽  
Vertex Operator ◽  
Operator Algebra ◽  
Correlation Functions ◽  
Vertex Operator Algebra ◽  
The Self ◽  
Genus Two ◽  
Complex Powers

We derive a formula for complex powers of the [Formula: see text]-function using the identities for a vertex operator algebra correlation functions in terms of [Formula: see text]-functions obtained in the self-sewing procedure of the torus to form a genus two Riemann surface.

scholarly journals Complex powers of hypoelliptic pseudodifferential operators

2007 ◽  
Vol 245 (2) ◽  
pp. 353-378 ◽  
Author(s):  
Ernesto Buzano ◽  
Fabio Nicola
Keyword(s):  
Pseudodifferential Operators ◽  
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
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