A note on Hardy spaces and bounded linear operators

作者：Rocha Pablo^*

来源：Georgian Mathematical Journal, 2018, 25(1): 73-76.

DOI：10.1515/gmj-2017-0060

• Hardy spaces
• atomic decomposition
• bounded linear operators

In this note we show that if f epsilon H-p(R-n) boolean AND L-s(R-n), where 0 < p <= 1 < s < infinity, then there exists a (p, infinity)-atomic decomposition which converges to f in L-s(R-n). From this result, we obtain that a bounded linear operator T on L-s(R-n) can be extended to a bounded operator from H-p(R-n) into L-p(R-n) if and only if T is bounded uniformly in L-p norm on all (p, infinity)-atoms. A similar result is also obtained from H-p(R-n) into H-p(R-n).

• 出版日期2018-3