On the Boundedness of Biparameter Littlewood-Paley gλ⁎-Function
Joint Authors
Source
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-12-22
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
Let m,n≥1 and let gλ1,λ2⁎ be the biparameter Littlewood-Paley gλ⁎-function defined by gλ1,λ2⁎fx = ∬R+m+1 t2/t2+x2-y2mλ2∬R+n+1 t1/t1+x1-y1nλ1×θt1,t2fy1,y22dy1dt1/t1n+1dy2dt2/t2m+11/2, λ1>1, λ2>1, where θt1,t2f is a nonconvolution kernel defined on Rm+n.
In this paper we show that the biparameter Littlewood-Paley function gλ1,λ2⁎ is bounded from L2Rn+m to L2Rn+m.
This is done by means of probabilistic methods and by using a new averaging identity over good double Whitney regions.
American Psychological Association (APA)
Cao, Mingming& Xue, Qingying. 2016. On the Boundedness of Biparameter Littlewood-Paley gλ⁎-Function. Journal of Function Spaces،Vol. 2016, no. 2016, pp.1-15.
https://search.emarefa.net/detail/BIM-1108591
Modern Language Association (MLA)
Cao, Mingming& Xue, Qingying. On the Boundedness of Biparameter Littlewood-Paley gλ⁎-Function. Journal of Function Spaces No. 2016 (2016), pp.1-15.
https://search.emarefa.net/detail/BIM-1108591
American Medical Association (AMA)
Cao, Mingming& Xue, Qingying. On the Boundedness of Biparameter Littlewood-Paley gλ⁎-Function. Journal of Function Spaces. 2016. Vol. 2016, no. 2016, pp.1-15.
https://search.emarefa.net/detail/BIM-1108591
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1108591