The Marcinkiewicz multiplier condition for bilinear operators

By Loukas Grafakos, Nigel J. Kalton. 2000

73 citations recorded by the source corpus.

This article is concerned with the question of whether Marcinkiewicz mul- tipliers onR 2n give rise to bilinear multipliers onR n R n . We show that this is not always the case. Moreover, we nd necessary and sucient conditions for such bilinear multipliers to be bounded. These conditions in particular imply that a slight logarithmic modica- tion of the Marcinkiewicz condition gives multipliers for which the corresponding bilinear operators are bounded on products of Lebesgue and Hardy spaces.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/20483e933e60cc23055e024e4274d714d62c45d4

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In Applied Mathematics

1. S. Hofmann
2. P. Auscher
3. Camil Muscalu
4. Terence Tao
5. C. Thiele
6. J. M. Martell
7. A. Mcintosh
8. A. Axelsson

In Mathematical Physics

1. S. Hofmann
2. P. Auscher
3. Camil Muscalu
4. Terence Tao
5. C. Thiele
6. J. M. Martell
7. A. Axelsson
8. Carlos E. Kenig

Citations in the corpus

• Lp estimates for the biest II. The Fourier case (2001, unknown): “1”
• Carleson measures, trees, extrapolation, and T(b) theorems (2001, background): “ng Lr by multilinear interpolation (see e.g. [6], [45], [33]). The continuous version of these dyadic paraproduct estimates can be found in, e.g. [14]-[19]; the version for r <1 was first proven in [30] (with some special cases in [9], [14]). It is possible to obtain the continuous estimates from ”
• MODULATION SPACES AND A CLASS OF BOUNDED MULTILINEAR PSEUDODIFFERENTIAL OPERATORS (2005, unknown): “B ´ ENYI, K. GR¨OCHENIG , C. HEIL, AND K. OKOUDJOU Marcinkiewicz multipliers, that use classical harmonic analysis techniques, see, e.g., [6], [12], [14].”