Article
Licensed
Unlicensed
Requires Authentication
New Proofs of Two-Weight Norm Inequalities for the Maximal Operator
-
D. Cruz-Uribe
Published/Copyright:
February 18, 2010
Abstract
We give a new and simpler proof of Sawyer's theorem characterizing the weights governing the two-weight, strong-type norm inequality for the Hardy-Littlewood maximal operator and the fractional maximal operator. As a further application of our techniques, we give new proofs of two sufficient conditions for such weights due to Wheeden and Sawyer.
Key words and phrases.: Weights; strong-type inequalities; Hardy–Littlewood maximal operator; fractional maximal operator
Received: 1999-07-19
Published Online: 2010-02-18
Published in Print: 2000-March
© Heldermann Verlag
You are currently not able to access this content.
You are currently not able to access this content.
Articles in the same Issue
- On Fourier Coefficients of Functions of Generalized Wiener Class
- Asymptotic Distribution of Eigenelements of the Basic Two-Dimensional Boundary-Contact Problems of Oscillation in Classical and Couple-Stress Theories of Elasticity
- New Proofs of Two-Weight Norm Inequalities for the Maximal Operator
- Convergent Rearrangements of Series of Vector-Valued Functions
- On the Convergence and Summability of N-Dimensional Fourier Series with Respect to the Walsh–Paley Systems in the Spaces LP([0, 1]N), p ∈ [1, + ∞]
- A Direct Boundary Integral Method for a Mobility Problem
- Unconditional Convergence of Random Series and the Geometry of Banach Spaces
- Quasi-Linearisation Methods for a Non-Linear Heat Equation with Functional Dependence
- On State Space Representations of AR-Models
- On a Nonlocal Boundary Value Problem for Second Order Nonlinear Singular Differential Equations
- On the Ito formula in a Banach Space
- On the Rearranged Block-Orthonormal Systems
- Classification of Singularities at Infinity of Polynomials of Degree 4 in Two Variables
- Qualitative Investigation of Two-Dimensional Chua's System
Keywords for this article
Weights;
strong-type inequalities;
Hardy–Littlewood maximal operator;
fractional maximal operator
Articles in the same Issue
- On Fourier Coefficients of Functions of Generalized Wiener Class
- Asymptotic Distribution of Eigenelements of the Basic Two-Dimensional Boundary-Contact Problems of Oscillation in Classical and Couple-Stress Theories of Elasticity
- New Proofs of Two-Weight Norm Inequalities for the Maximal Operator
- Convergent Rearrangements of Series of Vector-Valued Functions
- On the Convergence and Summability of N-Dimensional Fourier Series with Respect to the Walsh–Paley Systems in the Spaces LP([0, 1]N), p ∈ [1, + ∞]
- A Direct Boundary Integral Method for a Mobility Problem
- Unconditional Convergence of Random Series and the Geometry of Banach Spaces
- Quasi-Linearisation Methods for a Non-Linear Heat Equation with Functional Dependence
- On State Space Representations of AR-Models
- On a Nonlocal Boundary Value Problem for Second Order Nonlinear Singular Differential Equations
- On the Ito formula in a Banach Space
- On the Rearranged Block-Orthonormal Systems
- Classification of Singularities at Infinity of Polynomials of Degree 4 in Two Variables
- Qualitative Investigation of Two-Dimensional Chua's System
