Square functions, nontangential limits, and harmonic measure in codimension larger than $1$

2020 ◽  
Author(s):  
Guy David ◽  
Max Engelstein ◽  
Svitlana Mayboroda
Keyword(s):  
Harmonic Measure ◽  
Square Functions ◽  
Nontangential Limits

scholarly journals On the dimension of $p$-harmonic measure in space

2013 ◽  
Vol 15 (6) ◽  
pp. 2197-2256 ◽  
Author(s):  
John Lewis ◽  
Kaj Nyström ◽  
Andrew Vogel
Keyword(s):  
Harmonic Measure

A remark on bilinear Littlewood–Paley square functions

2014 ◽  
Vol 176 (4) ◽  
pp. 615-622 ◽  
Author(s):  
P. K. Ratnakumar ◽  
Saurabh Shrivastava
Keyword(s):  
Square Functions

scholarly journals UMD-Valued Square Functions Associated with Bessel Operators in Hardy and BMO Spaces

2014 ◽  
Vol 81 (3) ◽  
pp. 319-374 ◽  
Author(s):  
Jorge J. Betancor ◽  
Alejandro J. Castro ◽  
Lourdes Rodríguez-Mesa
Keyword(s):  
Square Functions ◽  
Bessel Operators ◽  
Bmo 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.

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