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A Hardy space related to the square root of the Poisson kernel

Jonatan Vasilis — 2010

Studia Mathematica

A real-valued Hardy space $H ¹_{\sqrt} () \subseteq L ¹ ()$ related to the square root of the Poisson kernel in the unit disc is defined. The space is shown to be strictly larger than its classical counterpart H¹(). A decreasing function is in $H ¹_{\sqrt} ()$ if and only if the function is in the Orlicz space LloglogL(). In contrast to the case of H¹(), there is no such characterization for general positive functions: every Orlicz space strictly larger than L log L() contains positive functions which do not belong to $H ¹_{\sqrt} ()$ , and no Orlicz space...

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