scholarly journals WEIGHTED NORM ESTIMATE FOR THE GENERAL HAAR SHIFT OPERATORS VIA ITERATING BELLMAN FUNCTION METHOD

2015 ◽  
Vol 31 (5) ◽  
pp. 635-652
Author(s):  
DAEWON CHUNG
Keyword(s):  
Function Method ◽  
Bellman Function ◽  
Weighted Norm ◽  
Norm Estimate ◽  
Shift Operators

A weighted weak-type bound for Haar multipliers

2018 ◽  
Vol 148 (3) ◽  
pp. 643-658
Author(s):  
Adam Osȩkowski
Keyword(s):  
Maximal Operator ◽  
Function Method ◽  
Dual Problem ◽  
Weak Type ◽  
Analogous Result ◽  
Type Inequality ◽  
Bellman Function ◽  
Weak Type Inequality ◽  
Image Position

We study a weighted maximal weak-type inequality for Haar multipliers that can be regarded as a dual problem of Muckenhoupt and Wheeden. More precisely, if Tε is the Haar multiplier associated with the sequence ε with values in [−1, 1], and is the r-maximal operator, then for any weight w and any function f on [0, 1) we havefor some constant Cr depending only on r. We also show that the analogous result does not hold if we replace by the dyadic maximal operator Md. The proof rests on the Bellman function method; using this technique we establish related weighted Lp estimates for p close to 1, and then deduce the main result by extrapolation arguments.

On the Bellman Function Method for Operators on Martingales

2021 ◽  
Vol 103 (3) ◽  
pp. 118-121
Author(s):  
V. A. Borovitskiy ◽  
N. N. Osipov ◽  
A. S. Tselishchev
Keyword(s):  
Function Method ◽  
Bellman Function

Higher rank Haar wavelet bases in spaces

2011 ◽  
Vol 18 (3) ◽  
pp. 517-532
Author(s):  
Tengiz Kopaliani
Keyword(s):  
Unconditional Basis ◽  
Function Method ◽  
Haar Wavelet ◽  
Bellman Function ◽  
Wavelet Bases ◽  
Wavelet System ◽  
Higher Rank

Abstract Using the Bellman function method, we prove that a Haar wavelet system of rank N (N ∈ ℕ, N ≥ 2) is an unconditional basis in , 1 < p < ∞, if and only if .

scholarly journals Sharp $$L_p$$ estimates for paraproducts on general measure spaces

2021 ◽  
Author(s):  
Adam Osękowski
Keyword(s):  
Function Method ◽  
Bellman Function ◽  
General Measure ◽  
Measure Spaces

AbstractThe paper contains the identification of the $$L_p$$ L p norms of paraproducts, defined on general measure spaces equipped with a dyadic-like structure. The proof exploits the Bellman function method.

THE ATOMISTIC GREEN'S FUNCTION METHOD FOR INTERFACIAL PHONON TRANSPORT

2014 ◽  
Vol 17 (N/A) ◽  
pp. 89-145 ◽  
Author(s):  
Sridhar Sadasivam ◽  
Yuhang Che ◽  
Zhen Huang ◽  
Liang Chen ◽  
Satish Kumar ◽  
...  
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Function Method ◽  
Phonon Transport ◽  
Green’S Function Method
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