多线性分数次积分算子交换子的有界性 Boundedness of multilinear fractional integral commutators期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

多线性分数次积分算子交换子的有界性

引用本文：

Wang Lei Pan Ting1 Dept. of Math.,Zhejiang Univ.,Hangzhou 310028,China. 2 Univ. of International Relation,Hangzhou 310015,China.. 多线性分数次积分算子交换子的有界性[J]. 高校应用数学学报(英文版), 2004, 19(2): 212-222. DOI: 10.1007/s11766-004-0056-3

作者姓名：

Wang Lei Pan Ting1 Dept. of Math. Zhejiang Univ. Hangzhou 310028 China. 2 Univ. of International Relation Hangzhou 310015 China.

作者单位：

Wang Lei Pan Ting1 Dept. of Math.,Zhejiang Univ.,Hangzhou 310028,China. 2 Univ. of International Relation,Hangzhou 310015,China.

摘要：

Ibαf ( x) =∫R ∏mj=1( bj( x) - bj( y) ) 1| x - y| n-αf ( y) dyare considered.The following priori estimates are proved.For 1 01Φ1t| {y∈Rn:| Ibαf( y) | >t}| 1q ≤csupt>01Φ1t| {y∈Rn:ML( log L) 1r ,α(‖b‖f ) ( y) >t}| 1q,where‖b‖=∏mj=1‖bj‖Oscexp Lrj,Φ( t) =t( 1 + log+t) 1r,1r =1r1+ ...+ 1rm,ML(…

关键词：

积分算子卢森堡标准多重线性转接器向量

Boundedness of multilinear fractional integral commutators

Wang Lei,Pan Ting. Boundedness of multilinear fractional integral commutators[J]. Applied Mathematics A Journal of Chinese Universities, 2004, 19(2): 212-222. DOI: 10.1007/s11766-004-0056-3

Authors:

Wang Lei Pan Ting

Affiliation:

Dept.of Math.,Zhejiang Univ.,Hangzhou 310028,China.;Univ.of International Relation,Hangzhou 310015,China.

Abstract:

By introducing a kind of maximal operator of fractional order associated with the mean Luxemburg norm and using the technique of Sharp function, multilinear commutators of fractional integral operator with vector symbol b = (b ₁,...b _m)defined by

$I_alpha ^b f(x) = int_R {left[ {prodlimits_{j = 1}^m {(b_j (x) - b_j (y))} } right]} frac{1}{{|x - y|^{n - alpha } }}f(y)user2{d}y$

are considered. The following priori estimates are proved. For 1<p<∞, there exists a constant c such that

$parallel I_alpha ^b fparallel L^p (R^n ) leqslant cparallel b parallel parallel M_{L(logL)} tfrac{l}{r},_alpha (f)parallel L^p (R_n ),$

$$parallel I_alpha ^b fparallel L^q (R^n ) leqslant cparallel b parallel parallel fparallel L^p (R_n ),$$

where 1<p<n/α,1/q=1/p−α/n,0<α<n,and

$begin{gathered} mathop {sup }limits_{t > 0} frac{1}{{Phi (tfrac{1}{t})}} left| { left{ {y in R^n : left| { I_a^b fleft( y right) } right| > t} right}} right|tfrac{1}{q} leqslant hfill c mathop {sup }limits_{t > 0} frac{1}{{Phi (tfrac{1}{t})}}left| {left{ {y in R^n :M_{L(logL)} tfrac{1}{r}_{,a} left( { left| { b } right| f} right)left( y right) > t} right}} right|tfrac{1}{q}, hfill end{gathered}$

where $parallel bparallel = prodnolimits_{j - 1}^m {parallel b_j parallel } _{Osc_{expL^{rj} } } ,Phi (1 + log^ + t)^{tfrac{1}{r}} ,frac{1}{r} = frac{1}{{r_1 }} + cdots + frac{1}{{r_m }},$ $M_{L(logL)} tfrac{1}{{r,alpha }}$ is an Orlicz type maximal operator.

Keywords:

fractional integral operator commutator sharp function Young function Luxemburg function.

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