Boundedness of integral operators from weighted Sobolev space to weighted Lebesgue space

2011 ◽  
Vol 56 (10-11) ◽  
pp. 1021-1038 ◽  
Author(s):  
R. Oinarov
Keyword(s):  
Sobolev Space ◽  
Lebesgue Space ◽  
Weighted Sobolev Space ◽  
Integral Operators ◽  
Weighted Lebesgue Space

scholarly journals On an extension of singular integrals along manifolds of finite type

2006 ◽  
Vol 2006 ◽  
pp. 1-16
Author(s):  
Abdelnaser Al-Hasan ◽  
Dashan Fan
Keyword(s):  
Sobolev Space ◽  
Finite Type ◽  
Singular Integral ◽  
Lebesgue Space ◽  
Compact Manifold ◽  
Singular Integrals ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Homogeneous Sobolev Space

We extend theLp-boundedness of a class of singular integral operators under theH1kernel condition on a compact manifold from the homogeneous Sobolev spaceL˙αp(ℝn)to the Lebesgue spaceLp(ℝn).

Optimal L 2 -decay of solutions to a cubic dissipative nonlinear Schrödinger equation

2021 ◽  
pp. 1-13
Author(s):  
Kita Naoyasu ◽  
Sato Takuya
Keyword(s):  
Sobolev Space ◽  
Global Solution ◽  
Initial Value Problem ◽  
Trivial Solution ◽  
Decay Estimate ◽  
Weighted Sobolev Space ◽  
The Other ◽  
Initial Value ◽  
Decay Of Solutions ◽  
Dissipative Nonlinearity

This paper presents the optimality of decay estimate of solutions to the initial value problem of 1D Schrödinger equations containing a long-range dissipative nonlinearity, i.e., λ | u | 2 u. Our aim is to obtain the two results. One asserts that, if the L 2 -norm of a global solution, with an initial datum in the weighted Sobolev space, decays at the rate more rapid than ( log t ) − 1 / 2 , then it must be a trivial solution. The other asserts that there exists a solution decaying just at the rate of ( log t ) − 1 / 2 in L 2 .

scholarly journals A parabolic system in a weighted Sobolev space

2007 ◽  
Vol 34 (2) ◽  
pp. 169-191
Author(s):  
Adam Kubica ◽  
Wojciech M. Zajączkowski
Keyword(s):  
Sobolev Space ◽  
Parabolic System ◽  
Weighted Sobolev Space

Sampling in a weighted Sobolev space

2012 ◽  
Vol 350 (21-22) ◽  
pp. 941-944
Author(s):  
Nestor G. Acala ◽  
Noli N. Reyes
Keyword(s):  
Sobolev Space ◽  
Weighted Sobolev Space
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