-BMO duality on graphs
On graphs satisfying the doubling property and the Poincaré inequality, we prove that the space is equal to , and therefore that its dual is BMO. We also prove the atomic decomposition for for p ≤ 1 close enough to 1.
and operator algebras.
functional calculus in real interpolation spaces
Let A be a linear closed densely defined operator in a complex Banach space X. If A is of type ω (i.e. the spectrum of A is contained in a sector of angle 2ω, symmetric around the real positive axis, and is bounded outside every larger sector) and has a bounded inverse, then A has a bounded functional calculus in the real interpolation spaces between X and the domain of the operator itself.
functional calculus in real interpolation spaces, II
Let A be a linear closed one-to-one operator in a complex Banach space X, having dense domain and dense range. If A is of type ω (i.e.the spectrum of A is contained in a sector of angle 2ω, symmetric about the real positive axis, and is bounded outside every larger sector), then A has a bounded functional calculus in the real interpolation spaces between X and the intersection of the domain and the range of the operator itself.
is a Grothendieck space
Sobolev spaces
spaces in tubes and distributional boundary values
-spaces of conjugate systems on local fields
spaces on bounded symmetric domains
spaces over open subsets of
H¹ and BMO for certain locally doubling metric measure spaces of finite measure
In a previous paper the authors developed an H¹-BMO theory for unbounded metric measure spaces (M,ρ,μ) of infinite measure that are locally doubling and satisfy two geometric properties, called “approximate midpoint” property and “isoperimetric” property. In this paper we develop a similar theory for spaces of finite measure. We prove that all the results that hold in the infinite measure case have their counterparts in the finite measure case. Finally, we show that the theory applies to a class...
H1/2 maps with values into the circle : minimal connections, lifting, and the Ginzburg–Landau equation
H² spaces of generalized half-planes
Haar null and non-dominating sets
We study the σ-ideal of Haar null sets on Polish groups. It is shown that on a non-locally compact Polish group with an invariant metric this σ-ideal is closely related, in a precise sense, to the σ-ideal of non-dominating subsets of . Among other consequences, this result implies that the family of closed Haar null sets on a Polish group with an invariant metric is Borel in the Effros Borel structure if, and only if, the group is locally compact. This answers a question of Kechris. We also obtain...
Hadamard's multiplication theorem - recent developments
Hahn-Banach theorem implies Riesz theorem.
Hahn-Banach type theorems for adjoint semigroups.
Hahn-Banach Type Theorems for Hypolinear Functionals.
Hajłasz-Sobolev type spaces and -energy on the Sierpinski gasket.
Half-liberated real spheres and their subspaces
We describe the quantum subspaces of Banica-Goswami's half-liberated real spheres, showing in particular that there is a bijection between the symmetric ones and the conjugation stable closed subspaces of the complex projective spaces.