|
|
|
|
On the Boundedness of Biparameter Littlewood-Paley g∗λ-Function
|
|
|
|
|
|
|
|
نویسنده
|
cao m. ,xue q.
|
|
منبع
|
journal of function spaces - 2016 - دوره : 2016 - شماره : 0
|
|
چکیده
|
Let m,n ≥ 1 and let g∗λ1,λ2 be the biparameter littlewood-paley g∗λ-function defined by g∗λ1,λ2(f)(x) = (∫∫ℝ+m+1 (t2/t2+x2-y2|))mλ2∫∫r+n+1 (t1/(t1+|x1-y1|))nλ1×|θt1,t2f(y1,y2)|2dy1dt1/t1n+1)(dy2dt2/t2m+1))1/2,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 g∗λ1,λ2 is bounded from l2(ℝn+m) to l2(ℝn+m). this is done by means of probabilistic methods and by using a new averaging identity over good double whitney regions. © 2016 mingming cao and qingying xue.
|
|
|
|
|
آدرس
|
school of mathematical sciences,beijing normal university,laboratory of mathematics and complex systems,ministry of education,beijing, China, school of mathematical sciences,beijing normal university,laboratory of mathematics and complex systems,ministry of education,beijing, China
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Authors
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|