Two-weight norm inequalities for the rough fractional integrals.
Hardy-Littlewood type inequalities for Laguerre series.
Convolution operators on Hardy spaces
We give sufficient conditions on the kernel K for the convolution operator Tf = K ∗ f to be bounded on Hardy spaces , where G is a homogeneous group.
L multipliers and their H-L estimates on the Heisenberg group.
We give a Hörmander-type sufficient condition on an operator-valued function M that implies the L-boundedness result for the operator T defined by (Tf)^ = Mf^ on the (2n + 1)-dimensional Heisenberg group H. Here ^ denotes the Fourier transform on H defined in terms of the Fock representations. We also show the H-L boundedness of T, ||Tf|| ≤ C||f||, for H under the same hypotheses of L-boundedness.
Almost everywhere convergence of Laguerre series
Calderón-Zygmund operators acting on generalized Carleson measure spaces
We study Calderón-Zygmund operators acting on generalized Carleson measure spaces and show a necessary and sufficient condition for their boundedness. The spaces are a generalization of BMO, and can be regarded as the duals of homogeneous Triebel-Lizorkin spaces as well.
Bilinear operators associated with Schrödinger operators
Let L = -Δ + V be a Schrödinger operator in and be the Hardy type space associated to L. We investigate the bilinear operators T⁺ and T¯ defined by , where T₁ and T₂ are Calderón-Zygmund operators related to L. Under some general conditions, we prove that either T⁺ or T¯ is bounded from to for 1 < p,q < ∞ with 1/p + 1/q = 1. Several examples satisfying these conditions are given. We also give a counterexample for which the classical Hardy space estimate fails.
The continuity of pseudo-differential operators on weighted local Hardy spaces
We first show that a linear operator which is bounded on with w ∈ A₁ can be extended to a bounded operator on the weighted local Hardy space if and only if this operator is uniformly bounded on all -atoms. As an application, we show that every pseudo-differential operator of order zero has a bounded extension to .
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