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The finite Hilbert transform in weighted spaces

  • Kari Astala (a1), Lassi Päivärinta (a2) and Eero Saksman (a1)

Abstract

The mapping properties of the finite Hilbert-transform (respectively the Hilbert transform on the half axis) are studied. Invertibility, surjectivity, injectivity and bounded ness from below of the transform are characterised in general weighted spaces. The results are applied to the restriction of the operator with logarithmic kernel.

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The finite Hilbert transform in weighted spaces

  • Kari Astala (a1), Lassi Päivärinta (a2) and Eero Saksman (a1)

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