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
We investigate the boundedness of singular and fractional integral operators on generalized Hardy spaces defined on spaces of homogeneous type, which are preduals of Campanato spaces with variable growth condition. To...We investigate the boundedness of singular and fractional integral operators on generalized Hardy spaces defined on spaces of homogeneous type, which are preduals of Campanato spaces with variable growth condition. To do this we introduce molecules with variable growth condition. Our results are new even for R^n case.展开更多
基金supported by Grant-in-Aid for Scientific Research (C) of Japan Society for the Promotion of Science (Grant No. 24540159)Grant-in-Aid for Young Scientists (B) of Japan Society for the Promotion of Science (Grant No. 24540085)
文摘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.
基金supported by Grant-in-Aid for Scientific Research (B) (Grant No. 15H03621), Japan Society for the Promotion of Science
文摘We investigate the boundedness of singular and fractional integral operators on generalized Hardy spaces defined on spaces of homogeneous type, which are preduals of Campanato spaces with variable growth condition. To do this we introduce molecules with variable growth condition. Our results are new even for R^n case.
