Journal of Mathematical Sciences

, Volume 85, Issue 2, pp 1767–1772

On a maximum principle for pseudocontinuable functions

  • A. B. Aleksandrov
Article

DOI: 10.1007/BF02355285

Cite this article as:
Aleksandrov, A.B. J Math Sci (1997) 85: 1767. doi:10.1007/BF02355285
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Abstract

Let Θ be an inner function and let α∈ℂ, |α|=1 Denote by σα the nonnegative singular measure whose Poisson integral is equal to\(\operatorname{Re} \frac{{\alpha + \Theta }}{{\alpha - \Theta }}\). A theorem of Clark provides a natural unitary operator Uα that identifies H2 ⊝Θ H2 with L2α). The following fact is established. Assume that f∈H2⊝Θ H2, 2<p≤+∞, α≠β. Then
$$\left\| f \right\|_{H^p } \leqslant C\left( {\alpha ,\beta ,p} \right)\left( {\left\| {U_\alpha f} \right\|_{L^p (\sigma _a )} + \left\| {U_B f} \right\|_{L^p (\sigma _\beta )} } \right)$$
.

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Copyright information

© Plenum Publishing Corporation 1997

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  • A. B. Aleksandrov

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