The final chapter of the book develops a general theory of singular integrals that generalizes and unifies these examples.
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This is one of the first general theories of multi-parameter singular integrals that goes beyond the product theory of singular integrals and their analogs. Multi-parameter Singular Integrals will interest graduate students and researchers working in singular integrals and related fields.
AM 62 by Eugene R. By addressing this in a quantitative way we obtain a holomorphic analog of the quantitative theory of sub-Riemannian geometry initiated by Nagel, Stein, and Wainger. We call this sub-Hermitian geometry.
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Moreover, we proceed more generally and obtain similar results for manifolds which have an associated formally integrable elliptic structure. This allows us to introduce a setting which generalizes both the real and complex theories. In this paper, we give optimal regularity for the coordinate charts which achieve this realization. We do this by generalizing Malgrange's proof of the Newlander-Nirenberg Theorem to this setting.ccomesacmenwilch.ml
Multi-parameter Singular Integrals. (AM-189), Volume I
Given a finite collection of C 1 vector fields on a C 2 manifold which span the tangent space at every point, we consider the question of when there is locally a coordinate system in which these vector fields have a higher level of smoothness. We give necessary and sufficient conditions for when there is a coordinate system in which the vector fields are smooth, or real analytic, or have Zygmund regularity of some finite order.
Furthermore, we provide a diffeomorphism invariant version of these theories. In the first paper, we study a particular coordinate system adapted to a collection of vector fields sometimes called canonical coordinates and present results related to the above questions which are not quite sharp; these results from the backbone of the series. The methods of the first paper are based on techniques from ODEs.
Analysis seminar: L^2 theory for a class of multi-parameter singular Radon transforms
In the second paper, we use additional methods from PDEs to obtain the sharp results. In the third paper, we prove results concerning real analyticity and use methods from ODEs. We establish optimal Lebesgue estimates for a class of generalized Radon transforms defined by averaging functions along polynomial-like curves. Here at Walmart.
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Celebratio Mathematica — Zygmund — Singular Integrals
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