Hardy Spaces on Ahlfors-Regular Quasi Metric Spaces by Ryan Alvarado & Marius Mitrea

Author:Ryan Alvarado & Marius Mitrea
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(5.403)

Going further, similar to argument which obtained the estimates in (5.382), we can use (5.360), the definition of , Lemma 5.13, and (2) in Theorem 2.​4, in order to write

(5.404)

where the last inequality in (5.404) relied on the fact that on X and the assumption p > q. Altogether, (5.403), (5.404), and (5.385) give

(5.405)

where in the last inequality of (5.405) we have enlarged the sum (as to eliminate any dependence on m 0) and made use of the estimate in (5.385). Hence, if is small enough so that we have

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