We prove that for all 1 ≤ p ≤ ∞, p 6= 2, the Lp spaces associated to two von Neumann algebrasM, N are isometrically isomorphic if and only if M and N are Jordan *-isomorphic. This follows from a noncommutative Lp Banach-Stone theorem: a specific decomposition for surjective isometries of noncommutative Lp spaces.

We establish the full range Gagliardo-Nirenberg and Caffarelli-Kohn-Nirenberg interpolation inequalities associated with Coulomb-Sobolev spaces for (fractional) derivative 0≤s≤1. As a result, we rediscover known type which were previously established in scale of Hs 0<s≤1 extend them Ws,p 0≤s≤1 1<p<+∞. Using these newly weighted inequalities, derive new family one body Hardy-Lieb-Thirring use it...

The approximation of road distances by the weighted lp distance measure has been studied in a series of papers ([5, 6], etc.) and it is argued with empirical study that lp distances weighted by an inflation factor tailored to given regions can better describe the irregularity in the transportation networks such as hill, bends, and are therefore superior to the weighted rectangular and Euclidean...

Some classical results due to Marcinkiewicz, Littlewood and Paley are proved for the Ciesielski-Fourier series. The Marcinkiewicz multiplier theorem is obtained for Lp spaces and extended to Hardy spaces. The boundedness of the Sunouchi operator on Lp and Hardy spaces is also investigated. 2000 AMS subject classifications: Primary 41A15, 42A45, 42B25, Secondary 42C10, 42B30.

We study decoupling in quasi-Banach spaces. We show that decoupling is permissible in some quasi-Banach spaces (e.g., Lp and Lp/Hp when 0 < p < 1) but fails in other spaces such as the Schatten ideal Sp when 0 < p < 1. We also relate our ideas to a possible extension of the Grothendieck inequality.

We consider the aff(1)-module structure on the spaces of bilinear differential operators acting on the spaces of weighted densities. We compute the first differential cohomology of the Lie superalgebra aff(1) with coefficients in space Dλ,ν;µ of bilinear differential operators acting on weighted densities. We study also the super analogue of this problem getting the same results.

‎In this paper, we provide a complete description of weighted composition operators between extended Lipschitz algebras on compact metric spaces. We give necessary and sufficient conditions for the injectivity and the sujectivity of these operators. We also obtain some sufficient conditions and some necessary conditions for a weighted composition operator between these spaces to be compact.