𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Cesàro Summability of Multi-dimensional Trigonometric-Fourier Series

✍ Scribed by Weisz, Ferenc (author)

Publisher
Academic Press Inc.
Year
1996
Tongue
English
Weight
163 KB
Volume
204
Category
Article
ISSN
0022-247X

No coin nor oath required. For personal study only.

✦ Synopsis

The d-dimensional classical Hardy spaces H T are introduced and it is shown p that the maximal operator of the Cesaro means of a distribution is bounded from Ž

that the supremum in the maximal operator is taken over a positive cone. As a consequence we obtain the summability result due to Marcinkievicz and Zygmund, Ž d . more exactly, the Cesaro means of a function f g L T converge a.e. to the `1 function in question, provided again that the limit is taken over a positive cone.

Ž . Similar results for the C, ␤ summability are also formulated.

📜 SIMILAR VOLUMES

Cesàro Summability of Two-Parameter Trig
Cesàro Summability of Two-Parameter Trigonometric-Fourier Series
✍ Ferenc Weisz 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 325 KB

The two-dimensional classical Hardy spaces H p (T\\_T) on the bidisc are introduced and it is shown that the maximal operator of the CesaÁ ro means of a distribution is bounded from H p (T\\_T) to L p (T 2 ) ( 3Â4 (T\\_T), L 1 (T 2 )) where the Hardy space H 1 > (T\\_T) is defined by the hybrid maxi