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Interpolation of Herz Spaces and Applications

✍ Scribed by Eugenio Hernández; Dachun Yang

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
793 KB
Volume
205
Category
Article
ISSN
0025-584X

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✦ Synopsis

C. HERZ introduced in [Hr] some new spaces to study properties of functions. An Interesting account, with many applications, of some particular cases of the generalized Herz spaces Is given in [BS]. In this paper we first identify the duals of the generalized Herz spaces. Then, we characterize their intermediate spaces when the complex method of interpolation for families of spaces Is used. Applications are given that show the boundedness of many operators on the generalized Herz paces.

(b) The non -homogeneous Herz space KrJ'(IR") is defined by K:>p(R") = { f E Lf,,(Rn) : IlfIIK;'P(IR") < M} )

📜 SIMILAR VOLUMES

Herz spaces and summability of Fourier t
Herz spaces and summability of Fourier transforms
✍ Hans G. Feichtinger; Ferenc Weisz 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 218 KB

## Abstract A general summability method is considered for functions from Herz spaces __K__^α^~__p,r__~ (ℝ^__d__^ ). The boundedness of the Hardy–Littlewood maximal operator on Herz spaces is proved in some critical cases. This implies that the maximal operator of the __θ__ ‐means __σ__^__θ__^ ~__