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On some metric topologies on Privalov spaces on the unit disk
[article]

2018
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arXiv
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pre-print

Let $N^p$ $(11$, we consider the class $N^p$ as the space $M^p$ equipped with the topology induced by the metric $\rho_p$ defined as $$ \rho_p(f,g) = \Bigg(\int_0^{2\pi}\log^p(1+M(f-g)(\theta))\, \frac{d\theta}{2\pi}\Bigg)^{1/p},\quad f,g\in M^p,\,\, {\mathrm where}\,\, Mf(\theta) = \sup_{0\leqslant r<1} \big\vert f \big(re^{i\theta})\big\vert.$$ On the other hand, we consider the class $N^p$ with the metric topology introduced by Me\v{s}trovi\'{c}, Pavi\'{c}evi\'{c} and Labudovi\'{c} (1999)

arXiv:1811.08956v1
fatcat:4pyol6oquvayzapc2l3nqceffi