Mixed-Norm Estimates for the k-Plane Transform

2012 ◽  
pp. 211-228
Author(s):  
Javier Duoandikoetxea ◽  
Virginia Naibo
Keyword(s):  
Mixed Norm ◽  
Norm Estimates

scholarly journals Mixed-norm estimates and symmetric geometric means

Positivity ◽  
2016 ◽  
Vol 21 (1) ◽  
pp. 343-358
Author(s):  
Wayne Grey
Keyword(s):  
Mixed Norm ◽  
Geometric Means ◽  
Norm Estimates

scholarly journals Mixed norm estimates for the Cesàro means associated with Dunkl–Hermite expansions

2017 ◽  
Vol 369 (10) ◽  
pp. 7021-7047 ◽  
Author(s):  
Pradeep Boggarapu ◽  
Luz Roncal ◽  
Sundaram Thangavelu
Keyword(s):  
Mixed Norm ◽  
Cesàro Means ◽  
Cesaro Means ◽  
Norm Estimates ◽  
Cesáro Means ◽  
Hermite Expansions

scholarly journals Estimates for Unimodular Multipliers on Modulation Hardy Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Jiecheng Chen ◽  
Dashan Fan ◽  
Lijing Sun ◽  
Chunjie Zhang
Keyword(s):  
Cauchy Problem ◽  
Hardy Spaces ◽  
Asymptotic Estimate ◽  
Nonlinear Partial Differential Equations ◽  
Modulation Spaces ◽  
Mixed Norm ◽  
Well Posedness ◽  
Cauchy Problems ◽  
Norm Estimates ◽  
The Cauchy Problem

It is known that the unimodular Fourier multiplierseit|Δ|α/2,α>0,are bounded on all modulation spacesMp,qsfor1≤p,q≤∞. We extend such boundedness to the case of all0<p,q≤∞and obtain its asymptotic estimate astgoes to infinity. As applications, we give the grow-up rate of the solution for the Cauchy problems for the free Schrödinger equation with the initial data in a modulation space, as well as some mixed norm estimates. We also study theMp1,qs→Mp2,qsboundedness for the operatoreit|Δ|α/2, for the case0<α≤2andα≠1.Finally, we investigate the boundedness of the operatoreit|Δ|α/2forα>0and obtain the local well-posedness for the Cauchy problem of some nonlinear partial differential equations with fundamental semigroupeit|Δ|α/2.

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