A converse Fatou theorem on homogeneous spaces

Mair, B.A.; Philipp, Stanton; Singman, David

doi:10.1215/ijm/1255988576

Search citation statements

Order By: Relevance

Paper Sections

Select...

Miscellaneous Notes1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

1998

2021

Publication Types

Select...

Article2

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

(1 citation statement)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Cf. [42, Theorem 2.9], [119][120][121][122]. See also A generalized Local Fatou Theorem by R. Wittmann (unpublished).…”

Section: Miscellaneous Notesmentioning

confidence: 99%

Foundations of Fatou Theory and a Tribute to the Work of E. M. Stein on Boundary Behavior of Holomorphic Functions

Biase

Krantz

2021

J Geom Anal

View full text Add to dashboard Cite

We lay the foundations of Fatou theory in one and several complex variables. We describe the main contributions contained in E. M. Stein’s book Boundary Behavior of Holomorphic Functions, published in 1972 and still a source of inspiration. We also give an account of his contributions to the study of the boundary behavior of harmonic functions. The point of this paper is not simply to exposit well-known ideas. Rather, we completely reorganize the subject in order to bring out the profound contributions of E. M. Stein to the study of the boundary behavior both of holomorphic and harmonic functions in one and several variables. In an appendix, we provide a self-contained proof of a new result which is relevant to the differentiation of integrals, a topic which, as witnessed in Stein’s work, and especially by the aforementioned book, has deep connections with the boundary behavior of harmonic and holomorphic functions.

show abstract

“…Cf. [42, Theorem 2.9], [119][120][121][122]. See also A generalized Local Fatou Theorem by R. Wittmann (unpublished).…”

Section: Miscellaneous Notesmentioning

confidence: 99%