an:03890073
Zbl 0558.41017
Colzani, Leonardo
Approximation in Hardy spaces
EN
Ann. Mat. Pura Appl., IV. Ser. 137, 207-215 (1984).
00149694
1984
j
41A17 42B30 41A30 41A63 41A65
maximal characterizations; entire functions; Jackson-Bernstein theorems; Hardy spaces; distributions; embedding theorems
The author studies the extension of the classical Jackson-Bernstein theorems to Hardy spaces \(H^ p({\mathbb{R}}^ N)\), \(0<p<\infty\), over the n-dimensional Euclidean space \({\mathbb{R}}^ N\). Direct and converse theorems are proved on approximation for distributions in a space \(\Lambda (p,{\mathbb{R}}^ N)\), the space of all distributions in \(H^ p({\mathbb{R}}^ N)\) equipped with a suitable norm, by means of entire- functions of exponential type (the analogue in \({\mathbb{R}}^ N\) of trigonometric polynomials). As consequences of the main theorems, certain results on embedding theorems for spaces \(\Lambda (p,{\mathbb{R}}^ N)\) are also deduced.
G.D.Dikshit