scholarly journals Products of power weights and Ap weights

1996 ◽  
Vol 15 (2) ◽  
pp. 141-151
Author(s):  
Randy Combs
Keyword(s):  
Ap Weights ◽  
Power Weights

scholarly journals Hardy's operator minus identity and power weights

2020 ◽  
Vol 279 (2) ◽  
pp. 108532
Author(s):  
Michał Strzelecki
Keyword(s):  
Power Weights

Weighted inequalities for the Stieltjes transform and the maximal spherical partial sum operator on radial functions

1995 ◽  
Vol 125 (1) ◽  
pp. 195-204
Author(s):  
Kenneth F. Andersen
Keyword(s):  
Fourier Transform ◽  
Lorentz Space ◽  
Sufficient Conditions ◽  
Weighted Inequalities ◽  
Stieltjes Transform ◽  
Radial Functions ◽  
Partial Sum ◽  
Power Weights ◽  
The Fourier Transform ◽  
Spherical Partial Sum

If TRf(x) is the spherical partial sum of the Fourier transform of f and T*f(x) = SUPR > 0 | TRf(x)|, sufficient conditions are given on the non-negative weight function ω(x) which ensure that T* restricted to radial functionsis bounded on the Lorentz space Lp,s(Rn,ω) into Lp,q(Rn, ω) For power weights, these conditions are also necessary. The weight pairs (u,v) for which the generalised Stieltjes transform Sλ is bounded from LP,S(R+, v)into Lp,q(R+, u)are also characterised. These are an essential ingredient for the study of T*.

scholarly journals Continuity of Weighted Operators, Muckenhoupt Ap Weights, and Steklov Problem for Orthogonal Polynomials

2020 ◽  
Author(s):  
Michel Alexis ◽  
Alexander Aptekarev ◽  
Sergey Denisov
Keyword(s):  
Orthogonal Polynomials ◽  
Unit Circle ◽  
Ap Weights ◽  
Steklov Problem ◽  
Muckenhoupt Class

Abstract We consider weighted operators acting on $L^p({\mathbb{R}}^d)$ and show that they depend continuously on the weight $w\in A_p({\mathbb{R}}^d)$ in the operator topology. Then, we use this result to estimate $L^p_w({\mathbb{T}})$ norm of polynomials orthogonal on the unit circle when the weight $w$ belongs to Muckenhoupt class $A_2({\mathbb{T}})$ and $p>2$. The asymptotics of the polynomial entropy is obtained as an application.

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