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.
Keywords
Mathematics
Hardy space
Subspace topology
Pure mathematics
Class (philosophy)
Cauchy distribution
Maximal function
Representation (politics)
Riesz representation theorem
Space (punctuation)
Function (biology)
Mathematical analysis
Combinatorics
Subject Areas
Advanced Harmonic Analysis Research
·Applied Mathematics ·Physical Sciences
advanced mathematical theories
·Mathematical Physics ·Physical Sciences
Mathematical Analysis and Transform Methods
·Applied Mathematics ·Physical Sciences
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