There are several characterizations of coarse embeddability of a discrete metric space into a Hilbert space. In this note we give such characterizations for general metric spaces. By applying these results to the spaces Lp(μ), we get their coarse embeddability into a Hilbert space for 0 < p < 2. This together with a theorem by Banach and Mazur yields that coarse embeddability into l2 and into L...

We study tent spaces on general measure spaces (Ω, μ). We assume that there exists a semigroup of positive operators on Lp(Ω, μ) satisfying a monotone property but do not assume any geometric/metric structure on Ω. The semigroup plays the same role as integrals on cones and cubes in Euclidean spaces. We then study BMO spaces on general measure spaces and get an analogue of Fefferman’s H1-BMO du...

In this talk we discuss a new connection between convex geometry and the theory of Lp-spaces. It appears that intersection bodies, one the main objects of convex geometry, are directly related to the concept of embedding of normed spaces in Lp with p < 0. This allows to get new geometric results by extending different facts about Lp-spaces to negative values of p. We present several application...

We show that non of the spaces ( ⊕∞ n=1 lp)lq , 1 ≤ p ̸= q < ∞ have a greedy basis. This solves a problem raised by Dilworth, Freeman, Odell and Schlumprect. Similarly, the spaces ( ⊕∞ n=1 lp)c0 , 1 ≤ p < ∞, and ( ⊕∞ n=1 co)lq , 1 ≤ q < ∞, do not have greedy bases. It follows from that and known results that a class of Besov spaces on Rn lack greedy bases as well.

STEIN and TAIFJLESON gave a characterization for f E Lp(IRn) to be in the spaces L i p ( a , Lp) and Zyg(a, L p ) in terms of their Poisson integrals. In this paper we extend their results to Lipschitz-Orlicz spaces Lip (cp, L M ) and Zygmund-Orlicz spaces Zyg (cp, L M ) and to the general function cp E P instead of the power function cp(t) = t a . Such results describe the behavior of the Lapl...

Some simplifications of Schaffer's girth and perimeter of the unit spheres are introduced. Their general properties are discussed, and they are used to study the lp, Lp spaces, uniformly nonsquare spaces, and their isomorphic classes. 1980 Mathematics subject classification (Amer. Math. Soc.) (1985 Revision): 46 B 20.

In this paper we introduce strong $I^K$-convergence of functions which is common generalization of strong $I^*$-convergence of functions in probabilistic metric spaces. We also define and study strong $I^{K}$-limit points of functions in same space.

in this paper, we prove the hyers-ulam stability in$beta$-homogeneous probabilistic modular spaces via fixed point method for the functional equation[f(x+ky)+f(x-ky)=f(x+y)+f(x-y)+frac{2(k+1)}{k}f(ky)-2(k+1)f(y)]for fixed integers $k$ with $kneq 0,pm1.$