scholarly journals Weighted Morrey Estimates for Multilinear Fourier Multiplier Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Songbai Wang ◽  
Yinsheng Jiang ◽  
Peng Li
Keyword(s):  
Fourier Multiplier ◽  
Morrey Spaces ◽  
Fourier Multipliers ◽  
Sobolev Regularity ◽  
Morrey Estimates ◽  
Fourier Multiplier Operators ◽  
Multiplier Operators

The multilinear Fourier multipliers and their commutators with Sobolev regularity are studied. The purpose of this paper is to establish that these operators are bounded on certain product Morrey spacesLp,k(ℝn). Based on the boundedness of these operators fromLp1(ω1)×⋯×Lpm(ωm)toLp(∏j=1m‍ωp/pj), we obtained that they are also bounded fromLp1,k(ω1)×⋯×Lpm,k(ωm)toLp,k(∏j=1m‍ωp/pj), with0<k<1,1<pj<∞,1/p=1/p1+⋯+1/pm, andωj∈Apj,j=1,…,m.

scholarly journals A Class of Unbounded Fourier Multipliers on the Unit Complex Ball

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Pengtao Li ◽  
Jianhao Lv ◽  
Tao Qian
Keyword(s):  
Unit Sphere ◽  
Fourier Multiplier ◽  
Differential Operators ◽  
Fourier Multipliers ◽  
Complex Ball ◽  
Fractional Differential ◽  
Fourier Multiplier Operators ◽  
Fractional Differential Operators ◽  
Multiplier Operators

We introduce a class of Fourier multiplier operatorsMbonn-complex unit sphere, where the symbolb∈Hs(Sω). We obtained the Sobolev boundedness ofMb. Our result implies that the operatorsMbtake a role of fractional differential operators on∂𝔹.

scholarly journals Some Weighted Estimates for Multilinear Fourier Multiplier Operators

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Zengyan Si
Keyword(s):  
Sobolev Spaces ◽  
Fourier Multiplier ◽  
Multilinear Operators ◽  
Multiplier Theorem ◽  
Weighted Estimates ◽  
Fourier Multiplier Operators ◽  
Multiplier Operators

We first provide a weighted Fourier multiplier theorem for multilinear operators which extends Theorem 1.2 in Fujita and Tomita (2012) by usingLr-based Sobolev spaces (1<r≤2). Then, by using a different method, we obtain a result parallel to Theorem 6.2 which is an improvement of Theorem 1.2 under assumption (i) in Fujita and Tomita (2012).

scholarly journals H-Distributions: An Extension ofH-Measures to anLp-LqSetting

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Nenad Antonić ◽  
Darko Mitrović
Keyword(s):  
Fourier Multiplier ◽  
Fourier Multiplier Operators ◽  
Multiplier Operators

We use the continuity of Fourier multiplier operators onLpto introduce theH-distributions—an extension ofH-measures in theLpframework. We apply theH-distributions to obtain anLpversion of the localisation principle and reprove the MuratLp-Lp′variant of div-curl lemma.

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