scholarly journals Modulation spaces, Wiener amalgam spaces, and Brownian motions

2011 ◽  
Vol 228 (5) ◽  
pp. 2943-2981 ◽  
Author(s):  
Árpád Bényi ◽  
Tadahiro Oh
Keyword(s):  
Modulation Spaces ◽  
Brownian Motions ◽  
Wiener Amalgam Spaces ◽  
Amalgam Spaces

scholarly journals Norm Inflation for Benjamin–Bona–Mahony Equation in Fourier Amalgam and Wiener Amalgam Spaces with Negative Regularity

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3145
Author(s):  
Divyang G. Bhimani ◽  
Saikatul Haque
Keyword(s):  
Initial Data ◽  
Modulation Spaces ◽  
Well Posedness ◽  
Wiener Amalgam Spaces ◽  
General Initial Data ◽  
Amalgam Spaces ◽  
Loss Of Regularity ◽  
Bbm Equation

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.

OPERATING FUNCTIONS ON MODULATION AND WIENER AMALGAM SPACES

2017 ◽  
Vol 230 ◽  
pp. 72-82 ◽  
Author(s):  
MASAHARU KOBAYASHI ◽  
ENJI SATO
Keyword(s):  
Open Problem ◽  
Composition Operators ◽  
Affirmative Answer ◽  
Modulation Spaces ◽  
Wiener Amalgam Spaces ◽  
Amalgam Spaces ◽  
Funct Anal

The goal of this paper is to characterize the operating functions on modulation spaces$M^{p,1}(\mathbb{R})$and Wiener amalgam spaces$W^{p,1}(\mathbb{R})$. This characterization gives an affirmative answer to the open problem proposed by Bhimani (Composition Operators on Wiener amalgam Spaces, arXiv: 1503.01606) and Bhimani and Ratnakumar (J. Funct. Anal.270(2016), pp. 621–648).

Singular convolution operators on Wiener amalgam spaces

2015 ◽  
Vol 13 (01) ◽  
pp. 1550003
Author(s):  
Meifang Cheng
Keyword(s):  
Modulation Spaces ◽  
Convolution Operators ◽  
Lebesgue Spaces ◽  
Wiener Amalgam Spaces ◽  
Amalgam Spaces

The purpose of this paper is to investigate some properties of the Wiener amalgam spaces. As applications, we study the boundedness properties of some singular convolution operators on such spaces. From our results, we will see that, besides modulation spaces, Wiener amalgam spaces are another good substitutions for Lebesgue spaces.

scholarly journals SHARPNESS OF SOME PROPERTIES OF WIENER AMALGAM AND MODULATION SPACES

2009 ◽  
Vol 80 (1) ◽  
pp. 105-116 ◽  
Author(s):  
ELENA CORDERO ◽  
FABIO NICOLA
Keyword(s):  
Modulation Spaces ◽  
Wiener Amalgam Spaces ◽  
Dilation Operator ◽  
Sharp Estimates ◽  
Amalgam Spaces ◽  
Scaling Arguments

AbstractWe prove sharp estimates for the dilation operator f(x)⟼f(λx), when acting on Wiener amalgam spaces W(Lp,Lq). Scaling arguments are also used to prove the sharpness of the known convolution and pointwise relations for modulation spaces Mp,q, as well as the optimality of an estimate for the Schrödinger propagator on modulation spaces.

scholarly journals COMPOSITION OPERATORS ON WIENER AMALGAM SPACES

2019 ◽  
Vol 240 ◽  
pp. 257-274
Author(s):  
DIVYANG G. BHIMANI
Keyword(s):  
Composition Operator ◽  
Composition Operators ◽  
Complex Function ◽  
Affirmative Answer ◽  
Modulation Spaces ◽  
Wiener Amalgam Spaces ◽  
Real Analytic ◽  
Amalgam Spaces ◽  
Open Question ◽  
Funct Anal

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).

p-FRAMES FOR SUBSPACES OF WIENER AMALGAMS ON A LOCALLY COMPACT ABELIAN GROUP

2003 ◽  
Vol 01 (04) ◽  
pp. 481-489
Author(s):  
S. S. PANDEY
Keyword(s):  
Abelian Group ◽  
Compact Abelian Group ◽  
Closed Subspace ◽  
Locally Compact Abelian Group ◽  
Locally Compact ◽  
Wiener Amalgam Spaces ◽  
Amalgam Spaces

We prove a theorem to characterize the p-frames for a shift invariant closed subspace of Wiener amalgam spaces [Formula: see text], 1 ≤ p ≤ q ≤ ∞, [Formula: see text] being a locally compact abelian group. Also, we show that a collection of translates under approximate conditions generaltes a p-frames for the space [Formula: see text].

scholarly journals Strong Summability of Fourier Transforms at Lebesgue Points and Wiener Amalgam Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Ferenc Weisz
Keyword(s):  
Fourier Series ◽  
Fourier Transforms ◽  
Lebesgue Point ◽  
Strong Summability ◽  
Wiener Amalgam Spaces ◽  
Wiener Amalgam Space ◽  
Almost Everywhere ◽  
Lebesgue Points ◽  
Amalgam Spaces

We characterize the set of functions for which strong summability holds at each Lebesgue point. More exactly, iffis in the Wiener amalgam spaceW(L1,lq)(R)andfis almost everywhere locally bounded, orf∈W(Lp,lq)(R)  (1<p<∞,1≤q<∞), then strongθ-summability holds at each Lebesgue point off. The analogous results are given for Fourier series, too.

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