Ap(ϕ) Weights, BMO(ϕ), and Calderón-Zygmund Operators of ϕ-Type

We introduce new classes of weights and BMO functions associated with a nondecreasing function ϕ of upper type β with β>0 and obtain the weighted norm inequalities for Calderón-Zygmund operators of ϕ-type and their commutators.

Weighted norm inequalities for a general maximal operator

Arkiv för matematik ◽

10.1007/bf02386127 ◽

1988 ◽

Vol 26 (1-2) ◽

pp. 327-340 ◽

Cited By ~ 2

Author(s):

Francisco J. Ruiz ◽

Jose L. Torrea

Keyword(s):

Maximal Operator ◽

Weighted Norm ◽

Weighted Norm Inequalities for Fractional Integrals with an Application to Mean Convergence of Laguerre Series

Journal of Approximation Theory ◽

10.1006/jath.1996.3089 ◽

1997 ◽

Vol 91 (1) ◽

pp. 84-102

Author(s):

E. Kochneff

Keyword(s):

Fractional Integrals ◽

Weighted Norm ◽

Norm Inequalities ◽

Mean Convergence ◽

Laguerre Series

Weighted norm inequalities for maximal operator of Fourier series

Advances in Operator Theory ◽

10.1007/s43036-021-00181-y ◽

2022 ◽

Vol 7 (1) ◽

Author(s):

Md. Nurul Molla ◽

Biswaranjan Behera

Keyword(s):

Fourier Series ◽

Maximal Operator ◽

Weighted Norm ◽

Weighted norm inequalities for certain integral operators. II

Proceedings of the American Mathematical Society ◽

10.1090/s0002-9939-1985-0806076-3 ◽

1985 ◽

Vol 95 (3) ◽

pp. 387-387 ◽

Cited By ~ 17

Author(s):

H. P. Heinig

Keyword(s):

Integral Operators ◽

Weighted Norm ◽

Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part I: General operator theory and weights

Advances in Mathematics ◽

10.1016/j.aim.2006.10.002 ◽

2007 ◽

Vol 212 (1) ◽

pp. 225-276 ◽

Cited By ~ 56

Author(s):

Pascal Auscher ◽

José María Martell

Keyword(s):

Operator Theory ◽

Elliptic Operators ◽

Weighted Norm ◽

General Operator ◽

Weighted Norm Inequalities for Fractional Integral Operators With Rough Kernel

Canadian Journal of Mathematics ◽

10.4153/cjm-1998-003-1 ◽

1998 ◽

Vol 50 (1) ◽

pp. 29-39 ◽

Cited By ~ 46

Author(s):

Yong Ding ◽

Shanzhen Lu

Keyword(s):

Integral Operator ◽

Fractional Integral ◽

Integral Operators ◽

Rough Kernel ◽

Degree Zero ◽

Weighted Norm ◽

Norm Inequalities ◽

Fractional Integral Operators ◽

Image Position

AbstractGiven function Ω on ℝn , we define the fractional maximal operator and the fractional integral operator by and respectively, where 0 < α < n. In this paper we study the weighted norm inequalities of MΩα and TΩα for appropriate α, s and A(p, q) weights in the case that Ω∈ Ls(Sn-1)(s> 1), homogeneous of degree zero.