As we have previously stated on a number of occasions, if g is integrable, its Hilbert transform is not necessarily integrable. Moreover, it can be even not locally integrable. When the Hilbert transform is integrable, we say that g is in the (real) Hardy space H1: = H1(ℝ). There are a variety of its characterizations (or, equivalently, definitions). The one given by means of the Hilbert transform is both important and convenient.
|Title of host publication||Pathways in Mathematics|
|Number of pages||29|
|State||Published - 2021|
|Name||Pathways in Mathematics|
Bibliographical notePublisher Copyright:
© 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.