Gâteaux derivatives and their applications to approximation in Lorentz spaces Γ p,w

2009 ◽  
Vol 282 (9) ◽  
pp. 1242-1264 ◽  
Author(s):  
Maciej Ciesielski ◽  
Anna Kamińska ◽  
Ryszard Płuciennik
Keyword(s):  
Lorentz Spaces ◽  
Gateaux Derivatives ◽  
Gâteaux Derivatives

scholarly journals INEQUALITIES IN TERMS OF THE GÂTEAUX DERIVATIVES FOR CONVEX FUNCTIONS ON LINEAR SPACES WITH APPLICATIONS

2011 ◽  
Vol 83 (3) ◽  
pp. 500-517 ◽  
Author(s):  
S. S. DRAGOMIR
Keyword(s):  
Convex Functions ◽  
Jensen’S Inequality ◽  
Jensen's Inequality ◽  
Linear Spaces ◽  
Divergence Measures ◽  
Gateaux Derivatives ◽  
Gâteaux Derivatives

AbstractSome inequalities in terms of the Gâteaux derivatives related to Jensen’s inequality for convex functions defined on linear spaces are given. Applications for norms, mean f-deviations and f-divergence measures are provided as well.

scholarly journals BOUNDS IN TERMS OF GÂTEAUX DERIVATIVES FOR THE WEIGHTED f-GINI MEAN DIFFERENCE IN LINEAR SPACES

2011 ◽  
Vol 83 (3) ◽  
pp. 420-434
Author(s):  
S. S. DRAGOMIR
Keyword(s):  
Symmetric Functions ◽  
Mean Difference ◽  
Linear Spaces ◽  
Inner Products ◽  
Gini Mean Difference ◽  
Gateaux Derivatives ◽  
Gâteaux Derivatives

AbstractSome bounds in terms of Gâteaux lateral derivatives for the weighted f-Gini mean difference generated by convex and symmetric functions in linear spaces are established. Applications for norms and semi-inner products are also provided.

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})}.

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.

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