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Orlicz-Hardy spaces and their duals 被引量:14
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作者 NAKAI Eiichi sawano yoshihiro 《Science China Mathematics》 SCIE 2014年第5期903-962,共60页
We establish the theory of Orlicz-Hardy spaces generated by a wide class of functions.The class will be wider than the class of all the N-functions.In particular,we consider the non-smooth atomic decomposition.The rel... We establish the theory of Orlicz-Hardy spaces generated by a wide class of functions.The class will be wider than the class of all the N-functions.In particular,we consider the non-smooth atomic decomposition.The relation between Orlicz-Hardy spaces and their duals is also studied.As an application,duality of Hardy spaces with variable exponents is revisited.This work is different from earlier works about Orlicz-Hardy spaces H(Rn)in that the class of admissible functions is largely widened.We can deal with,for example,Ф(r)≡(rp1(log(e+1/r))q1,0〈r≤1,r^p2 (log(e+r))q2,r〉1,with p1,p2∈(0,∞)and q1,q2∈(.∞,∞),where we shall establish the boundedness of the Riesz transforms on H(Rn).In particular,is neither convex nor concave when 0〈p1〈1〈p2〈∞,0〈p21〈p1〈∞or p1=p2=1 and q1,q20.If(r)≡r(log(e+r))q,then H(Rn)=H(logH)q(Rn).We shall also establish the boundedness of the fractional integral operators I of order∈(0,∞).For example,I is shown to be bounded from H(logH)1^1-α/n(Rn)to Ln/(n-α)(log L)(Rn)for 0〈α〈n. 展开更多
关键词 Hardy space Orlicz space atomic decomposition Campanato space bounded mean oscillation
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Generalized Morrey spaces and trace operator 被引量:6
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作者 NAKAMURA Shohei NOI Takahiro sawano yoshihiro 《Science China Mathematics》 SCIE CSCD 2016年第2期281-336,共56页
The theory of generalized Besov-Morrey spaces and generalized Triebel-Lizorkin-Morrey spaces is developed. Generalized Morrey spaces, which Mizuhara and Nakai proposed, are equipped with a parameter and a function. Th... The theory of generalized Besov-Morrey spaces and generalized Triebel-Lizorkin-Morrey spaces is developed. Generalized Morrey spaces, which Mizuhara and Nakai proposed, are equipped with a parameter and a function. The trace property is one of the main focuses of the present paper, which will clarify the role of the parameter of generalized Morrey spaces. The quarkonial decomposition is obtained as an application of the atomic decomposition. In the end, the relation between the function spaces dealt in the present paper and the foregoing researches is discussed. 展开更多
关键词 Morrey space trace operator DECOMPOSITION
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