A genuine analogue of the Wiener Tauberian theorem for some Lorentz spaces on SL(2,ℝ)

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Tapendu Rana
Keyword(s):  
Tauberian Theorem ◽  
Lorentz Spaces

AbstractIn this paper, we prove a genuine analogue of the Wiener Tauberian theorem for {L^{p,1}(G)} ({1\leq p<2}), with {G=\mathrm{SL}(2,\mathbb{R})}.

Classical Tauberian Theorems for the (C; 1; 1) Summability Method

2014 ◽  
Vol 0 (0) ◽  
Author(s):  
Ümit Totur
Keyword(s):  
Tauberian Theorem ◽  
Summability Method ◽  
Subject Classification ◽  
Tauberian Theorems ◽  
Double Sequences ◽  
Littlewood Theorem

Abstract In this paper we generalize some classical Tauberian theorems for single sequences to double sequences. One-sided Tauberian theorem and generalized Littlewood theorem for (C; 1; 1) summability method are given as corollaries of the main results. Mathematics Subject Classification 2010: 40E05, 40G0

scholarly journals Lorentz spaces in action on pressureless systems arising from models of collective behavior

2021 ◽  
Author(s):  
Raphaël Danchin ◽  
Piotr Bogusław Mucha ◽  
Patrick Tolksdorf
Keyword(s):  
Initial Data ◽  
Collective Behavior ◽  
Existence And Uniqueness ◽  
Maximal Regularity ◽  
Parabolic Systems ◽  
Lorentz Spaces ◽  
Regularity Estimate ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Time Existence

AbstractWe are concerned with global-in-time existence and uniqueness results for models of pressureless gases that come up in the description of phenomena in astrophysics or collective behavior. The initial data are rough: in particular, the density is only bounded. Our results are based on interpolation and parabolic maximal regularity, where Lorentz spaces play a key role. We establish a novel maximal regularity estimate for parabolic systems in $$L_{q,r}(0,T;L_p(\Omega ))$$ L q , r ( 0 , T ; L p ( Ω ) ) spaces.

Complete space-like hypersurfaces in locally symmetric Lorentz spaces

2004 ◽  
Vol 49 (2) ◽  
pp. 231-247 ◽  
Author(s):  
Jin Ok Baek ◽  
Qing-Ming Cheng ◽  
Young Jin Suh
Keyword(s):  
Lorentz Spaces ◽  
Complete Space

scholarly journals GENERALIZATION OF THE EFFECTIVE WIENER–IKEHARA THEOREM

2013 ◽  
Vol 09 (08) ◽  
pp. 2091-2128 ◽  
Author(s):  
SZILÁRD GY. RÉVÉSZ ◽  
ANNE de ROTON
Keyword(s):  
Laplace Transform ◽  
Tauberian Theorem ◽  
Error Term ◽  
Effective Version ◽  
Slow Decrease ◽  
Asymptotic Evaluation ◽  
The Laplace Transform

We consider the classical Wiener–Ikehara Tauberian theorem, with a generalized condition of slow decrease and some additional poles on the boundary of convergence of the Laplace transform. In this generality, we prove the otherwise known asymptotic evaluation of the transformed function, when the usual conditions of the Wiener–Ikehara theorem hold. However, our version also provides an effective error term, not known thus far in this generality. The crux of the proof is a proper, asymptotic variation of the lemmas of Ganelius and Tenenbaum, also constructed for the sake of an effective version of the Wiener–Ikehara theorem.

scholarly journals The convolution algebraH1(R)

2010 ◽  
Vol 8 (2) ◽  
pp. 167-179 ◽  
Author(s):  
R. L. Johnson ◽  
C. R. Warner
Keyword(s):  
Banach Algebra ◽  
Maximal Ideal ◽  
Tauberian Theorem ◽  
Singular Integrals ◽  
Approximate Identity ◽  
Maximal Ideal Space ◽  
Ideal Space

H1(R) is a Banach algebra which has better mapping properties under singular integrals thanL1(R) . We show that its approximate identity sequences are unbounded by constructing one unbounded approximate identity sequence {vn}. We introduce a Banach algebraQthat properly lies betweenH1andL1, and use it to show thatc(1 + lnn) ≤ ||vn||H1≤Cn1/2. We identify the maximal ideal space ofH1and give the appropriate version of Wiener's Tauberian theorem.

On the boundedness of classical operators on weighted lorentz spaces

1998 ◽  
Vol 5 (2) ◽  
pp. 177-200 ◽  
Author(s):  
Y. Rakotondratsimba
Keyword(s):  
Lorentz Spaces ◽  
Weighted Lorentz Spaces
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