We study the backward shift operator on Hilbert spaces Hα (for α ≥ 0) which are norm equivalent to the Dirichlet-type spaces Dα. Although these operators are unitarily equivalent to the adjoints of the forward shift operator on certain weighted Bergman spaces, our approach is direct and completely independent of the standard Cauchy duality. We employ only the classical Hardy space theory and an...

We give various equivalent formulations to the (partially) open problem about Lboundedness of Bergman projections in tubes over cones. Namely, we show that such boundedness is equivalent to the duality identity between Bergman spaces, A ′ = (Ap)∗, and also to a Hardy type inequality related to the wave operator. We introduce analytic Besov spaces in tubes over cones, for which such Hardy inequa...

Abstract The inequalities of Hardy-Littlewood and Riesz say that certain integrals involving products of two or three functions increase under symmetric decreasing rearrangement. It is known that these inequalities extend to integrands of the form F (u1, . . . , um) where F is supermodular; in particular, they hold when F has nonnegative mixed second derivatives ∂i∂jF for all i 6= j. This paper...

We describe some elements of the theory of semigroups generated by second order differential operators needed to study the Hardy-type space H1 L related to the time independent Schrödinger operator L = −∆+ V , with V ≥ 0 a potential satisfying a reverse Hölder inequality. Its dual space is a BMO-type space BMOL, that turns out to be the suitable one for the versions of some classical operators ...

We establish a Maz’ya type capacitary inequality which resolves special case of conjecture by David R. Adams. As consequence, we obtain several equivalent norms for Choquet integrals associated to Bessel or Riesz capacities. This enables us bounds the Hardy–Littlewood maximal function in sublinear setting.