Hardy’s inequality on Hardy spaces. (English) Zbl 1362.26018

Ho, Kwok-Pun

Proc. Japan Acad., Ser. A 92, No. 10, 125-130 (2016).

Summary: We extend the Hardy inequalities to the classical Hardy spaces and the rearrangement-invariant Hardy spaces.

MSC:

26D10	Inequalities involving derivatives and differential and integral operators
42B30	\(H^p\)-spaces
46E30	Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
47B38	Linear operators on function spaces (general)

Keywords:

Hardy inequality; Hardy space; rearrangement-invariant; atomic decomposition; interpolation