Abstract
Grand Hardy class H+p), p > 1, is defined and some properties of functions belonging to this class are studied in this work. Namely, the analogs of the Riesz and Smirnov theorems as well as the Cauchy’s formula for representation of function are proved. Necessary and sufficient condition for the validity of Riesz theorem in grand Hardy spaces H+p), p > 1, is found. Subspace GH+p)of the grand Hardy space H+p)generated by this condition is defined.
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