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Interpolation Theorems of Marcinkiewicz and Riesz-Thorin

Ali Taheri

in Function Spaces and Partial Differential Equations: Volume 1 - Classical Analysis

Published in print:
2015
Published Online:
September 2015
ISBN:
9780198733133
eISBN:
9780191797712
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198733133.003.0006
Subject:
Mathematics, Analysis

This chapter introduces the two main interpolations theorems: Marcinkiewicz and Riesz-Thorin. It also presents a number of important applications. The chapter includes a discussion of weak-Lebesgue ... More


How to Go beyond the Case hlin(φ‎) ≥ 5

Isroil A. Ikromov and Detlef Müller

in Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194)

Published in print:
2016
Published Online:
October 2017
ISBN:
9780691170541
eISBN:
9781400881246
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691170541.003.0007
Subject:
Mathematics, Geometry / Topology

This chapter mostly considers the domains of type Dsubscript (l), which are in some sense “closest” to the principal root jet, since it turns out that the other domains Dsubscript (l) with l ≥ 2 are ... More


Improved Estimates by Means of Airy-Type Analysis

Isroil A. Ikromov and Detlef Müller

in Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194)

Published in print:
2016
Published Online:
October 2017
ISBN:
9780691170541
eISBN:
9781400881246
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691170541.003.0005
Subject:
Mathematics, Geometry / Topology

This chapter turns to the proof of a proposition from the previous chapter. Given the operators appearing in that proposition, this chapter establishes the endpoint result thereof by means of Stein's ... More


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