COMPLEX GEODESICS, THEIR BOUNDARY REGULARITY, AND A HARDY-LITTLEWOOD-TYPE LEMMA

Bharali, Gautam (2016) COMPLEX GEODESICS, THEIR BOUNDARY REGULARITY, AND A HARDY-LITTLEWOOD-TYPE LEMMA. In: ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 41 (1). pp. 253-263.

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Abstract

We begin by giving an example of a smoothly bounded convex domain that has complex geodesics that do not extend continuously up to partial derivative D. This example suggests that continuity at the boundary of the complex geodesics of a convex domain Omega (sic) C-n, n >= 2, is affected by the extent to which partial derivative Omega curves or bends at each boundary point. We provide a sufficient condition to this effect (on C-1-smoothly bounded convex domains), which admits domains having boundary points at which the boundary is infinitely flat. Along the way, we establish a Hardy-Littlewood-type lemma that might be of independent interest.

Item Type:	Journal Article
Publication:	ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA
Publisher:	SUOMALAINEN TIEDEAKATEMIA
Additional Information:	Copy right for this article belongs to the SUOMALAINEN TIEDEAKATEMIA, MARIANKATU 5, 00170 HELSINKI, FINLAND
Keywords:	Boundary regularity; complex geodesics; Hardy-Littlewood lemma
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	02 Apr 2016 05:22
Last Modified:	02 Apr 2016 05:22
URI:	http://eprints.iisc.ac.in/id/eprint/53595

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