Ming-Yi Lee

Hardy spaces and theTb theorem

AbstractIt is well-known that Calderón-Zygmund operators T are bounded on Hp forn

A wavelet characterization for the dual of weighted Hardy spaces

frac{n}{{n + 1}}< p leqslant 1

Fractional integrals on weighted Hardy spaces

n provided T*(1) = 0. In this article, it is shown that if T*(b) = 0, where b is a para-accretive function, T is bounded from the classical Hardy space Hp to a new Hardy space Hbp. To develop an Hbp theory, a discrete Calderón-type reproducing formula and Plancherel-Pôlya-type inequalities associated to a para-accretive function are established. Moreover, David, Journé, and Semmes’ result [9] about the LP, 1 < p < ∞, boundedness of the Littlewood-Paley g function associated to a para-accretive function is generalized to the case of p ≤ 1. A new characterization of the classical Hardy spaces by using more general cancellation adapted to para-accretive functions is also given. These results complement the celebrated Calderón-Zygmund operator theory.

Generalized Calderón–Zygmund operators on homogeneous groups and applications

In this article, we establish a new atomic decomposition for f ∈ Lw ∩ H p w , where the decomposition converges in Lw-norm rather than in the distribution sense. As applications of this decomposition, assuming that T is a linear operator bounded on Lw and 0 < p ≤ 1, we obtain (i) if T is uniformly bounded in L p w-norm for all w-p-atoms, then T can be extended to be bounded from H p w to L p w ; (ii) if T is uniformly bounded in H p w-norm for all w-p-atoms, then T can be extended to be bounded on H p w; (iii) if T is bounded on H p w , then T can be extended to be bounded from H p w to L p w .

CARLESON MEASURE SPACES ASSOCIATED TO PARA-ACCRETIVE FUNCTIONS

We define the weighted Carleson measure space CMO p /ω using wavelets, where the weight function w belongs to the Muckenhoupt class. Then we show that CMO p / ω is the dual space of the weighted Hardy space H p / ω by using sequence spaces. As an application, we give a wavelet characterization of BMOω.

Tb theorem on product spaces

A molecular characterization of the weighted Herz-type Hardy spaces HK˙qn(1/p-1/q),p(w, w) and HKqn(1/p-1/q),p(w, w) is given, by which the boundedness of the Hilbert transform and the Riesz transforms are proved on these space for 0 < p ≤ 1. These results are obtained by first deriving that the convolution operator Tf = k * f is bounded on the weighted Herz-type Hardy spaces.

The molecular characterization of weighted Hardy spaces

Abstract In this paper, applying the atomic decomposition and molecular characterization of the real weighted Hardy spaces H w p ( R n ) , we give the weighted boundedness of the homogeneous fractional integral operator T Ω,α from H w p p ( R n ) to L q w q ( R n ) , and from H w p p ( R n ) toxa0 H w q q ( R n ) .

Large-Time Behavior of Solutions for the Boltzmann Equation with Hard potentials

There are two folds of this article. The first part is concentrating on estimates for generalized Calderón–Zygmund operators acting on Hardy spaces H p (G). Here G is a simply connected homogeneous Lie group. We also obtained estimates on the spaces L ∞(G) and BMO p (G). The second part of this article is applications of results from the first part to the -Neumann problem on bounded, smoothly pseudoconvex domains in C n+1. We obtain H p estimates for the Calderón operator when G = H n , the n-dimensional Heisenberg group.