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Usually, the condition that T is bounded on L2(ℝn) is assumed to prove the boundedness of an operator T on a Hardy space. With this assumption, one only needs to… Click to show full abstract
Usually, the condition that T is bounded on L2(ℝn) is assumed to prove the boundedness of an operator T on a Hardy space. With this assumption, one only needs to prove the uniformly boundness of T on atoms, since T(f)= ∑i λiT(ai), provided that f = ∑i λiai in L2 (ℝn), where ai is an L2 atom of this Hardy space. So far, the L2 atomic decomposition of local Hardy spaces hp(ℝn), 0 > p ≤ 1, hasn’t been established. In this paper, we will solve this problem, and also show that hp(ℝn) can also be characterized by discrete Littlewood-Paley functions.
Keywords:
littlewood paley;
discrete littlewood;
hardy spaces;
local hardy;
atomic decomposition;
decomposition local
Journal Title: Acta Mathematica Sinica, English Series
Year Published: 2019
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Journal Title: Acta Mathematica Sinica, English Series
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!