Endpoint multiplier theorems of Marcinkiewicz type

0 Endpoint Multiplier Theorems of Marcinkiewicz Type

We establish sharp (H 1 , L 1,q) and local (L log r L, L 1,q) mapping properties for rough one-dimensional multipliers. In particular, we show that the multipliers in the Marcinkiewicz multiplier theorem map H 1 to L 1,∞ and L log 1/2 L to L 1,∞ , and that these estimates are sharp.

The Marcinkiewicz Multiplier Condition for Bilinear Operators

This article is concerned with the question of whether Marcinkiewicz multipliers on R2n give rise to bilinear multipliers on R×R. We show that this is not always the case. Moreover, we find necessary and sufficient conditions for such bilinear multipliers to be bounded. These conditions in particular imply that a slight logarithmic modification of the Marcinkiewicz condition gives multipliers f...

On Marcinkiewicz-Zygmund-Type Inequalities

We investigate the relationships between the Marcinkiewicz-Zygmund-type inequalities and certain shifted average operators. Applications to the mean boundedness of a quasi-interpolatory operator in the case of trigonometric polynomials, Jacobi polynomials, and Freud polynomials are presented.

Stability theorems for semi{groups via Multiplier theorems

Boundedness of higher-order Marcinkiewicz-Type integrals

Let A be a function with derivatives of order m and DγA∈ Λ̇β (0 < β < 1, |γ| =m). The authors in the paper proved that ifΩ∈ Ls(Sn−1) (s≥ n/(n−β)) is homogeneous of degree zero and satisfies a vanishing condition, then both the higher-order Marcinkiewicz-type integral μΩ and its variation μ̃ A Ω are bounded from L p(Rn) to Lq(Rn) and from L1(Rn) to Ln/(n−β),∞(Rn), where 1 < p < n/β and 1/q = 1/p− ...