wiener amalgam spaces
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Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3145
Author(s):  
Divyang G. Bhimani ◽  
Saikatul Haque

We consider the Benjamin–Bona–Mahony (BBM) equation of the form ut+ux+uux−uxxt=0,(x,t)∈M×R where M=T or R. We establish norm inflation (NI) with infinite loss of regularity at general initial data in Fourier amalgam and Wiener amalgam spaces with negative regularity. This strengthens several known NI results at zero initial data in Hs(T) established by Bona–Dai (2017) and the ill-posedness result established by Bona–Tzvetkov (2008) and Panthee (2011) in Hs(R). Our result is sharp with respect to the local well-posedness result of Banquet–Villamizar–Roa (2021) in modulation spaces Ms2,1(R) for s≥0.


Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 331
Author(s):  
Junjian Zhao ◽  
Marko Kostić ◽  
Wei-Shih Du

In this paper, we establish generalized sampling theorems, generalized stability theorems and new inequalities in the setting of shift-invariant subspaces of Lebesgue and Wiener amalgam spaces with mixed-norms. A convergence theorem of general iteration algorithms for sampling in some shift-invariant subspaces of Lp→(Rd) are also given.


2020 ◽  
Vol 50 (5) ◽  
pp. 1647-1659
Author(s):  
Ahmet Turan Gürkanlı

2019 ◽  
Vol 68 (3) ◽  
pp. 451-482 ◽  
Author(s):  
Weichao Guo ◽  
Jiecheng Chen ◽  
Dashan Fan ◽  
Guoping Zhao

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 528 ◽  
Author(s):  
Hans G. Feichtinger ◽  
Justin Feuto

The purpose of this paper is to characterize the pre-dual of the spaces introduced by I. Fofana on the basis of Wiener amalgam spaces. These spaces have a specific dilation behaviour similar to the spaces L α ( R d ) . The characterization of the pre-dual will be based on the idea of minimal invariant spaces (with respect to such a group of dilation operators).


2019 ◽  
Vol 240 ◽  
pp. 257-274
Author(s):  
DIVYANG G. BHIMANI

For a complex function $F$ on $\mathbb{C}$, we study the associated composition operator $T_{F}(f):=F\circ f=F(f)$ on Wiener amalgam $W^{p,q}(\mathbb{R}^{d})\;(1\leqslant p<\infty ,1\leqslant q<2)$. We have shown $T_{F}$ maps $W^{p,1}(\mathbb{R}^{d})$ to $W^{p,q}(\mathbb{R}^{d})$ if and only if $F$ is real analytic on $\mathbb{R}^{2}$ and $F(0)=0$. Similar result is proved in the case of modulation spaces $M^{p,q}(\mathbb{R}^{d})$. In particular, this gives an affirmative answer to the open question proposed in Bhimani and Ratnakumar (J. Funct. Anal. 270(2) (2016), 621–648).


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