Translator Disclaimer
September 2020 Elliptic problems and holomorphic functions in Banach spaces
Wolfgang Arendt, Manuel Bernhard, Marcel Kreuter
Illinois J. Math. 64(3): 331-347 (September 2020). DOI: 10.1215/00192082-8591584

Abstract

In the first part, we show that a Banach space-valued function f is holomorphic (harmonic) if and only if it is dominated by an L loc 1 function and there exists a separating set W X ' such that f , x ' is holomorphic (harmonic) for all x ' W . This improves a known result which requires f to be locally bounded. In the second part, we consider classical results in the L p theory for elliptic differential operators of second order. In the vector-valued setting, these results are shown to be equivalent to the UMD property.

Citation

Download Citation

Wolfgang Arendt. Manuel Bernhard. Marcel Kreuter. "Elliptic problems and holomorphic functions in Banach spaces." Illinois J. Math. 64 (3) 331 - 347, September 2020. https://doi.org/10.1215/00192082-8591584

Information

Received: 4 May 2019; Revised: 23 March 2020; Published: September 2020
First available in Project Euclid: 1 July 2020

zbMATH: 07235507
MathSciNet: MR4132595
Digital Object Identifier: 10.1215/00192082-8591584

Subjects:
Primary: 35J25
Secondary: 30A99, 31C05, 46B20

Rights: Copyright © 2020 University of Illinois at Urbana-Champaign

JOURNAL ARTICLE
17 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.64 • No. 3 • September 2020
Back to Top