Removable singularities for hardy spaces

• In this paper we study removable singularities for Hardy spaces of analytic funtions on general domains. Two different definitions are given. For compact sets they turn out to be equal and moreover independent of the surrounding domain, as was proved by D. A Hejhal For non-compact sets the difference between the definitions is studied. A survey of the present knowledge is given, except for the special cases of singularities lying on curves and singularities being self-similar Cantor sets, which the author deals with in other papers. Among the results is the non-removability for Hp of sets with dimension greater than ρ. 0 < ρ < 1. Many counterexamples are provided and the Hp capacities are introduced and studied.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

Analytic capacity; analytic continuation; analytic function; capacity; conformal; invariant; Hardy class; Hp-capacity; Hp-space; harmonic majorant; harmonic measure; Hausdorff dimension; Hausdorff measure; holomorphie function; logarithmic capacity; newtonian capacity; Riesz capacity; removable singularity

MATHEMATICS

MATEMATIK

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