Hardy-Littlewood, Hausdorff-Young-Paley inequalities, and L-L Fourier multipliers on compact homogeneous manifolds

Fourier Multipliers on Weighted L-spaces

In his 1986 paper in the Rev. Mat. Iberoamericana, A. Carbery proved that a singular integral operator is of weak type (p, p) on Lp(Rn) if its lacunary pieces satisfy a certain regularity condition. In this paper we prove that Carbery’s result is sharp in a certain sense. We also obtain a weighted analogue of Carbery’s result. Some applications of our results are also given.

Littlewood-Paley g-Functions and Multipliers for the Laguerre Hypergroup

Fourier Series Acceleration and Hardy-littlewood Series

We discuss the effects of the δ2 and Lubkin acceleration methods on the partial sums of Fourier Series. We construct continuous, even Hölder continuous functions, for which these acceleration methods fail to give convergence. The constructed functions include some interesting trigonometric series whose properties were investigated by Hardy and Littlewood.

Boundedness for Multilinear Littlewood-Paley Operators on Hardy and Herz-Hardy Spaces

Let T be a Calderon-Zygmund operator, a classical result of Coifman, Rochberg and Weiss (see [7]) states that the commutator [b, T ] = T (bf)−bTf (where b ∈ BMO(Rn)) is bounded on Lp(Rn) for 1 < p < ∞; Chanillo (see [2]) proves a similar result when T is replaced by the fractional integral operator. However, it was observed that [b, T ] is not bounded, in general, from Hp(Rn) to Lp(Rn) for p ≤ ...

Boundedness for Multilinear Commutator of Littlewood-paley Operator on Hardy and Herz-hardy Spaces

Let 0 < q < ∞ and Lqloc(R n) = {f q is locally integrable on Rn}. Suppose f ∈ Lloc(R), B = B(x0, r) = {x ∈ Rn : |x − x0| < r} denotes a ball of Rn centered at x0 and having radius r, write fB = |B|−1 ∫ B f(x)dx and f #(x) = supx∈B |B|−1 ∫ B |f(x) − fB|dx < ∞. f is said to belong to BMO(R n), if f# ∈ L∞(Rn) and define ||f ||BMO = ||f||L∞ . Let T be the Calderón-Zygmund singular integral operator...