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Translations of functions iv vector Hardy classes on the unit disk

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Michalak A.

Instytut Matematyczny Polskiej Akademii Nauk

CONTENTS Introduction...................................................................................................5 0. Preliminaries................................................................................................7 1. Fundamental properties of harmonic vector functions...............................13 2. Hardy spaces of vector functions...............................................................15 Relations between scalar and vector Hardy classes...................................15 The factorization theorem for $H^p(𝔻,X)$...................................................19 Nontangential limits of functions in $h^p(𝔻,X)$...........................................22 Properties of functions in $h^p(𝕋,X)$..........................................................27 3. Spaces $h^p(𝔻,X)$ and $M_p(𝕋,X)$..........................................................29 4. The sets of translates of harmonic functions..............................................33 5. Translations of functions from Hardy classes..............................................37 6. Translations of functions from Smirnov classes...........................................41 7. Translations of measures from $M_p(G,X)$................................................43 8. A criterion of uncomplementability of $L^p(λ_G,X)$ in $M_p(G,X)$.............53 9. Pettis integrability of the translation function for vector measures...............64 References...................................................................................................77

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1 Michalak A.

1 1996

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Translations of functions iv vector Hardy classes on the unit disk