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Monatshefte für Mathematik

, Volume 176, Issue 4, pp 615–622 | Cite as

A remark on bilinear Littlewood–Paley square functions

  • P. K. Ratnakumar
  • Saurabh ShrivastavaEmail author
Article

Abstract

The aim of this note is to point out that the results proved in Bernicot and Shrivastava (Indiana Univ Math J 60(1):233–268, 2011) and Ratnakumar and Shrivastava (Proc Am Math Soc 140(12):4285–4293, 2012), for bilinear square functions associated with symbols of the form \(\varphi (x-n)\), extend to a far more general family of bilinear multiplier symbols \(\phi _n\), supported in disjoint cubes \(Q_n\).

Keywords

Bilinear multipliers Littlewood–Paley square functions Sobolev spaces 

Mathematics Subject Classification (2000)

42A45 42B15 42B25 

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Copyright information

© Springer-Verlag Wien 2014

Authors and Affiliations

  1. 1.School of MathematicsHarish-Chandra Research InstituteAllahabadIndia
  2. 2.Department of MathematicsIndian Institute of Science Education and ResearchBhopalIndia

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