scholarly journals Sharp Weighted Bounds for Multilinear Fractional Type Operators Associated with Bergman Projection

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Juan Zhang ◽  
Senhua Lan ◽  
Qingying Xue
Keyword(s):  
Maximal Function ◽  
Bergman Projection ◽  
Weighted Estimates ◽  
Fractional Maximal Function ◽  
Multiple Weights ◽  
Fractional Type

We first introduce the multiple weights which are suitable for the study of Bergman type operators. Then, we give the sharp weighted estimates for multilinear fractional Bergman operators and fractional maximal function.

scholarly journals Weighted Vector-Valued Inequalities for a Class of Multilinear Singular Integral Operators

2018 ◽  
Vol 61 (2) ◽  
pp. 413-436 ◽  
Author(s):  
Guoen Hu ◽  
Kangwei Li
Keyword(s):  
Singular Integral ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Maximal Operators ◽  
Weighted Estimates ◽  
Multilinear Singular Integral ◽  
Multiple Weights ◽  
Vector Valued

AbstractIn this paper, some weighted vector-valued inequalities with multiple weights $A_{\vec P}$ (ℝmn)are established for a class of multilinear singular integral operators. The weighted estimates for the multi(sub)linear maximal operators which control the multilinear singular integral operators are also considered.

scholarly journals Weighted estimates for the Berezin transform and Bergman projection on the unit ball

2016 ◽  
Vol 286 (3-4) ◽  
pp. 1465-1478 ◽  
Author(s):  
Rob Rahm ◽  
Edgar Tchoundja ◽  
Brett D. Wick
Keyword(s):  
Unit Ball ◽  
Berezin Transform ◽  
Bergman Projection ◽  
Weighted Estimates

scholarly journals On weighted estimates for Stein's maximal function

1996 ◽  
Vol 54 (1) ◽  
pp. 35-39 ◽  
Author(s):  
Hendra Gunawan
Keyword(s):  
Maximal Function ◽  
Unit Sphere ◽  
Surface Measure ◽  
Weighted Estimates ◽  
Mellin Transformation ◽  
Transformation Approach ◽  
Image Position

Let φ denote the normalised surface measure on the unit sphere Sn−1. We shall be interested in the weighted Lp estimate for Stein's maximal function Mφf, namelywhere w is an Ap weight, especially for 1 < p ≤ 2. Using the Mellin transformation approach, we prove that the estimate holds for every weight wδ where w ∈ Ap and 0 ≤ δ < (p(n − 1) − n)/(n(p − 1)), for n ≥ 3 and n/(n − 1) < p ≤ 2.

scholarly journals Sharp integral estimates for the fractional maximal function and interpolation

2006 ◽  
Vol 44 (2) ◽  
pp. 309-326 ◽  
Author(s):  
Natan Kruglyak ◽  
Evgeny A. Kuznetsov
Keyword(s):  
Maximal Function ◽  
Fractional Maximal Function
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