We give a new proof of the sharp one weight $ L^ p $ inequality for any operator $ T $ that
can be approximated by Haar shift operators such as the Hilbert transform, any Riesz …

Let hR denote an L∞ normalized Haar function adapted to a dyadic rectangle R⊂[0, 1] d.
We show that for choices of coefficients α (R), we have the following lower bound on the L∞ …

In this paper we prove the Jones factorization theorem and the Rubio de Francia
extrapolation theorem for matrix $\mathcal A_p $ weights. These results answer …

We give a self-contained proof of the A2 conjecture, which claims that the norm of any
Calderón–Zygmund operator is bounded by the first degree of the A2 norm of the weight …

For any Calderón–Zygmund operator T the following sharp estimate is obtained for 1<
p<∞:\left ‖ T\right ‖ _ L^ p_ (w) ≦ cv_ p\left ‖ w\right ‖ _ A_ 1, where …

For any Calderón–Zygmund operator, any weight, and, the operator is bounded as a map
from into weak-. The interest in questions of this type goes back to the beginnings of the …

Though multi-parameter Hardy space theory has been well developed in the past half
century, not much has been studied for a local Hardy space theory in the multi-parameter …

Let h R denote an L∞-normalized Haar function adapted to a dyadic rectangle R⊂[0, 1] 3.
We show that there is a positive η< 1/2 so that for all integers n and coefficients α (R), we …

After the celebrated work of L. Hörmander on the one-parameter pseudo-differential
operators, the applications of pseudo-differential operators have played an important role in …

We apply the discrete version of Calderón's identity and Littlewood–Paley–Stein theory with
weights to derive the (H^p_w,H^p_w) and (H^p_w,L^p_w)(0<p≤1) boundedness for …