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Using discrete decomposition techniques, bilinear operators are naturally associated with trilinear tensors. An intrinsic size condition on the entries of such tensors is introduced and is used to… (More)

- Oliver Dragicevic, Loukas Grafakos, Maŕıa Cristina Pereyra, Stefanie Petermichl
- 2004

We obtain sharp weighted Lp estimates in the Rubio de Francia extrapolation theorem in terms of the Ap characteristic constant of the weight. Precisely, if for a given 1 < r < ∞ the norm of a… (More)

- Loukas Grafakos, JOSÉ MARÍA MARTELL
- 2003

Two versions of Rubio de Francia’s extrapolation theorem for multivariable operators of functions are obtained. One version assumes an initial estimate with different weights in each space and… (More)

Convolution type Calderón-Zygmund singular integral operators with rough kernels p.v. Ω(x)/|x| are studied. A condition on Ω implying that the corresponding singular integrals and maximal singular… (More)

- Loukas Grafakos, LIU LiGuang, YANG DaChun
- 2008

Let X be an RD-space, i.e., a space of homogeneous type in the sense of Coifman and Weiss, which has the reverse doubling property. Assume that X has a “dimension” n. For α ∈ (0,∞) denote by H α(X ),… (More)

- XUAN THINH DUONG, Loukas Grafakos, Lixin Yan
- 2009

We obtain endpoint estimates for multilinear singular integral operators whose kernels satisfy regularity conditions significantly weaker than those of the standard Calderón-Zygmund kernels. As a… (More)

This article is concerned with the question of whether Marcinkiewicz multipliers on R give rise to bilinear multipliers on R ×Rn. We show that this is not always the case. Moreover we find necessary… (More)

- Loukas Grafakos
- 1992

We continue the study of multilinear operators given by products of finite vectors of Calderón-Zygmund operators. We determine the set of all r ≤ 1 for which these operators map products of Lebesgue… (More)

- Loukas Grafakos, AKIHIKO MIYACHI, N. Tomita
- 2011

In this paper, we prove the L2-boundedness of multilinear Fourier multiplier operators with multipliers of limited smoothness. As a result, we can extend Calderón and Torchinsky’s result in the… (More)

A multilinear version of the Boyd interpolation theorem is proved in the context of quasi-normed rearrangement-invariant spaces. A multilinear Marcinkiewicz interpolation theorem is obtained as a… (More)