Functional calculus estimates for Tadmor–Ritt operators

Hörmander Functional Calculus for Poisson Estimates

Abstract. The aim of the article is to show a Hörmander spectral multiplier theorem for an operator A whose kernel of the semigroup exp(−zA) satisfies certain Poisson estimates for complex times z. Here exp(−zA) acts on L(Ω), 1 < p < ∞, where Ω is a space of homogeneous type with the additional condition that the measure of annuli is controlled. In most of the known Hörmander type theorems in t...

A new functional calculus for noncommuting operators

In this paper we use the notion of slice monogenic functions [2] to define a new functional calculus for an n-tuple T of not necessarily commuting operators. This calculus is different from the one discussed in [5] and it allows the explicit construction of the eigenvalue equation for the n-tuple T based on a new notion of spectrum for T . Our functional calculus is consistent with the Riesz-Du...

Functional Calculus for Non-Commuting Operators

Sobolev Space Estimates and Symbolic Calculus for Bilinear Pseudodifferential Operators

Bilinear operators are investigated in the context of Sobolev spaces and various techniques useful in the study of their boundedness properties are developed. In particular, several classes of symbols for bilinear operators beyond the so called CoifmanMeyer class are considered. Some of the Sobolev space estimates obtained apply to both the bilinear Hilbert transform and its singular multiplier...

Non commutative functional calculus: bounded operators

In this paper we develop a functional calculus for bounded operators defined on quaternionic Banach spaces. This calculus is based on the notion of slice-regularity, see [4], and the key tools are a new resolvent operator and a new eigenvalue problem. AMS Classification: 47A10, 47A60, 30G35.