Abstract
Let γ be a non-rectifiable closed Jordan curve in C, which is merely assumed to be d-summable (1 < d < 2) in the sense of Harrison and Norton [7]. We are interested in the so-called jump problem over γ, which is that of finding an analytic function in C having a prescribed jump across the curve. The goal of this note is to show that the sufficient solvability condition of the jump problem given by ν > d/2 , being the jump function defined in and satisfying a Hölder condition with exponent ν, 0 < ν ≤ 1, cannot be weakened on the whole class of dsummable curves.
Original language | English |
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Pages (from-to) | 26-33 |
Number of pages | 8 |
Journal | Communications in Mathematical Analysis |
Volume | 12 |
Issue number | 2 |
State | Published - 2012 |
Externally published | Yes |
Keywords
- Analytic functions
- Cauchy integral
- Fractional dimension
- Jump problem
- Non-rectifiable curve