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Commutators of Bilinear Pseudodifferential Operators and Lipschitz Functions
Commutators of bilinear pseudodifferential operators and the operation of multiplication by a Lipschitz function are studied. The bilinear symbols of...
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A Generalized Beurling Theorem for Some Lie Groups
For any real numbers p,q ≥ 1, we present in this paper a ( p, q )-generalized version of Beurling’s uncertainty principle for ℝ n , which largely extends...
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Lp Theory of Pseudo-Differential Operators
In this chapter we present a brief description of the basic concepts and results of the L p theory of pseudo-differential operators, which may be...
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Generalized Born-Jordan distributions and applications
One of the most popular time-frequency representations is certainly the Wigner distribution. Its quadratic nature is, however, at the origin of...
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Time Regularity for Local Weak Solutions of the Heat Equation on Local Dirichlet Spaces
We study the time regularity of local weak solutions of the heat equation in the context of local regular symmetric Dirichlet spaces. Under two basic...
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Variational Formulations
In this chapter we will discuss the variational formulation for boundary integral equations and its connection to the variational solution of partial...
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Continuity of pseudodifferential operators on mixed-norm Lebesgue spaces
Mixed-norm Lebesgue spaces found their place in the study of some questions in the theory of partial differential equations, as it can be seen from...
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The Heisenberg Group and Its Relatives in the Work of Elias M. Stein
We survey the work of Elias M. Stein in the field of analysis on the Heisenberg group and other nilpotent Lie groups, together with its applications...
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Boundary value problems of elliptic and parabolic type with boundary data of negative regularity
We study elliptic and parabolic boundary value problems in spaces of mixed scales with mixed smoothness on the half-space. The aim is to solve...
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Classical Analytic Formalism
Section 19.3 is devoted to the statement and proof of the complex-analytic version of the Stationary Phase expansion formula (cf. the Appendix), not...
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The Gevrey smoothing effect for the spatially inhomogeneous Boltzmann equations without cut-off
In this article we study the Gevrey regularization effect for the spatially inhomogeneous Boltzmann equation without angular cutoff. This equation is...
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Fundamentals
This introductory chapter contains a brief review of the theory of real and complex manifolds, including the basics of holomorphic approximation...
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Maximal regularity
The present chapter is one of the central ones of this book project. Maximal regularity provides a link between the general theory of operator-valued...
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Banach Space Theory
In this chapter we present some basic concepts and results from Functional Analysis (Banach Space Theory). In Sect. 3.2 we introduce the terminology...
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Introduction
We give a short overview of the scopes of both the theory of rough paths and the theory of regularity structures. The main ideas are introduced and...
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\(L^p\)-Boundedness and \(L^p\)-Nuclearity of Multilinear Pseudo-differential Operators on \({\mathbb {Z}}^n\) and the Torus \({\mathbb {T}}^n\)
In this article, we begin a systematic study of the boundedness and the nuclearity properties of multilinear periodic pseudo-differential operators...