Benjamin Muckenhoupt

Maximal functions on classical Lorentz spaces and Hardy’s inequality with weights for nonincreasing functions

A characterization is given of a class of classical Lorentz spaces on which the Hardy Littlewood maximal operator is bounded. This is done by determining the weights for which Hardys inequality holds for nonincreasing functions. An alternate characterization, valid for nondecreasing weights, is also derived.

Weighted norm inequalities for singular and fractional integrals

Inequalities of the form 11 lxl cTf 1,q < C 11 lxl af 11, are proved for certain well-known integral transforms, T, in En. The transforms considered include Calder6n-Zygmund singular integrals, singular integrals with variable kernel, fractional integrals and fractional integrals with variable kernel.

Weighted Norm Inequalities for Classical Operators

The principle problem to be discussed here is the determination of all pairs of non-negative functions U(x), V(x) such that

L2 multipliers with power weights

\int_{ - \infty }^\infty {\left| {{\text{Sf}}\left( {\text{x}} \right)} \right|^{\text{P}} {\text{U}}\left( {\text{x}} \right){\text{dx}} \leqslant {\text{C}}\int_{ - \infty }^\infty {\left| {{\text{Tf}}\left( {\text{x}} \right)} \right|^{\text{P}} {\text{V}}\left( {\text{x}} \right){\text{dx}}} }

Weak type estimates for Bochner-Riesz spherical summation multipliers

(1.1) where 1≤p<∞ S and T are two given operators and C is a constant independent of f. Results described here will be primarily on the real line; there are periodic analogues of most and almost all have been or can be generalized to Rn. There are also closely related Hp results valid for all positive p.

Two-weight norm inequalities for the cesàro means of hermite expansions

Facts and definitions An absolute value estimate for

Necessity conditions for ^{} multipliers with power weights

3(1-y)\leq 2(1-x)

Norm Inequalities Relating the Hilbert Transform to the Hardy-Littlewood Maximal Function

A basic estimate for