Frame Decompositions of Form-Valued Hardy Spaces
John E. Gilbert, Jeffrey A. Hogan, Joseph D. Lakey · 2018
Wavelets have appeared in the theory of Hardy H p -spaces for a long time, though the precise connection has been recognized only in the past few years. For example, when Hardy spaces consist of functions analytic in the upper half-plane, Meyer [Ml, p. 22] reinterprets Lusin’s representation ( 13.1.1 ) F ( z ) = ∫ ∫ ℝ + 2 ( z − ζ ¯ ) − 2 α ( ζ ) d u d v , ( ζ = u , i v , v > 0 ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315139548/2af6e4bd-72bf-419b-b1f3-52d645c48a21/content/eq1907.tif"/>