As it was shown by Shen, the Riesz transforms associated to Schrödinger operator L=−Δ+V are not bounded on Lp(Rd)-spaces for all p,1<p<∞, under only assumption that potential satisfies a reverse Hölder condition of order d/2, d≥3. Furthermore, they p in some finite interval type (1,p0), so can be expected preserve regularity spaces. In this work we search kind minimal additional conditions obta...

We show that the range of a contractive projection on a Lebesgue-Bochner space of Hilbert valued functions Lp(H) is isometric to a p-direct sum of Hilbertvalued Lp-spaces. We explicit the structure of contractive projections. As a consequence for every 1 < p < ∞ the class Cp of p-direct sums of Hilbertvalued Lp-spaces is axiomatizable (in the class of all Banach spaces).

We introduce 2 parameter variants Lp,q of the Lebesgue spaces, to gain separate control on the asymptotic behaviour (p) and the local behaviour (q). Thus they behave w.r.t. p like the spaces lp and w.r.t. q like the spaces Lq on a probability space. Convolution behaves very well on those spaces.

We present an Itô formula for the Lp-norm of jump processes having stochastic differentials in Lp-spaces. The main results extend well-known theorems Krylov to case with jumps, which can be used prove existence and uniqueness Lp-spaces SPDEs driven by Lévy processes.

In this paper we sharpen a theorem of Gröchenig about embedding weighted Lp-spaces into a modulation space. The theorem is closely related to the problem of pointwise convergence in the Poisson summation formula (PSF). We also show that this sharp version is optimal in some sense by extending a family of counterexamples to PSF also due to Gröchenig. The proof requires new techniques, namely the...

Overview of the field. NoncommutativeLp-spaces are at the heart of this conference. These spaces have a long history going back to pioneering works by von Neumann, Dixmier and Segal. They are the analogues of the classical Lebesgue spaces of pintegrable functions, where now functions are replaced by operators. These spaces have been investigated for operator algebras with a trace, and then arou...

We consider the problem of reconstruction of entire functions of exponential type τ that are elements of certain weighted Lp(μ)-spaces from their values and the values of their derivatives up to order ν. In this paper we extend the interpolation results of [24] in which the case ν = 1 was solved. Using the theory of de Branges spaces we find a discrete set Tτ,ν of points on the real line and a ...