In this article,atomic decompositions and the duals of some B-valued r.v.se- quence spaces are investigated.The results show that it closely depends on the geometrical properties of the sequence that take values in.
In 2011,Dekel et al.developed highly geometric Hardy spaces H^(p)(Θ),for the full range 0<p≤1,which are constructed by continuous multi-level ellipsoid coverΘof R^(n) with high anisotropy in the sense that the e...In 2011,Dekel et al.developed highly geometric Hardy spaces H^(p)(Θ),for the full range 0<p≤1,which are constructed by continuous multi-level ellipsoid coverΘof R^(n) with high anisotropy in the sense that the ellipsoids can change shape rapidly from point to point and from level to level.The authors obtain the finite atomic decomposition characterization of Hardy spaces H^(p)(Θ)and as an application,the authors prove that given an admissible triplet(p,q,l)with 1≤q≤∞,if T is a sublinear operator and uniformly bounded elements of some quasi-Banach space B for maps all(p,q,l)-atoms with q<∞(or all continuous(p,q,l)-atoms with q=∞),then T uniquely extends to a bounded sublinear operator from H^(p)(Θ)to B.These results generalize the known results on the anisotropic Hardy spaces of Bownik et al.展开更多
A theory recently developed by the present authors is applied to the study of the effect of elastic energy due to atomic size factor on the transformation behaviour of binary solid solutions. lt is found that elastic ...A theory recently developed by the present authors is applied to the study of the effect of elastic energy due to atomic size factor on the transformation behaviour of binary solid solutions. lt is found that elastic interaction energy (EIE), which is a part of the total elastic energy plays a key role in both ordering elastic interaction ordering (EIO) and spinodal decomposition. The present study gives a reasonable explanation to the historical dilemmas, "elastic energy paradox" and "atomic size factor paradox . By solving these confusing problems, the coexistence of ordering (EIO) and decomposition, which has been regarded as impossible by conventional theories. can be well understood. The mechanism is as follows: lowering of elastic energy demands EIO, and such an ordering provides a driving force for spinodal decomposition. Therefore, in alloys with large atomic size factor, spinodal decomposition is preceded and induced by ordering. Ordering and spinodal decomposition are thus closely related processes to each展开更多
Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting...Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.展开更多
We study unboundedness of smoothness Morrey spaces on bounded domains ? ? R^n in terms of growth envelopes. It turns out that in this situation the growth envelope function is finite—in contrast to the results obtain...We study unboundedness of smoothness Morrey spaces on bounded domains ? ? R^n in terms of growth envelopes. It turns out that in this situation the growth envelope function is finite—in contrast to the results obtained by Haroske et al.(2016) for corresponding spaces defined on R^n. A similar effect was already observed by Haroske et al.(2017), where classical Morrey spaces M_(u,p)(?) were investigated. We deal with all cases where the concept is reasonable and also include the tricky limiting cases. Our results can be reformulated in terms of optimal embeddings into the scale of Lorentz spaces L_(p,q)(?).展开更多
We introduce the variable integral and the smooth exponent Besov spaces associated to non-negative self-adjoint operators.Then we give the equivalent norms via the Peetre type maximal functions and atomic decompositio...We introduce the variable integral and the smooth exponent Besov spaces associated to non-negative self-adjoint operators.Then we give the equivalent norms via the Peetre type maximal functions and atomic decomposition of these spaces.展开更多
Suppose that g(f)are bi-parameter Littlewood-Paley square functions which were introduced by H.Martikainen.It is known that the L^2(R^n×R^m)boundedness and the H1(R^n×R^m)-L1(R^n×R^m)boundedness of g(f)...Suppose that g(f)are bi-parameter Littlewood-Paley square functions which were introduced by H.Martikainen.It is known that the L^2(R^n×R^m)boundedness and the H1(R^n×R^m)-L1(R^n×R^m)boundedness of g(f)have been proved by H.Martikainen and by Z.Li and Q.Xue,respectively.In this paper,we apply the vector-valued theory,the atomic decomposition of product Hardy spaces,and Journe’s covering lemma to show that g(f)are bounded from H^p(R^n×R^m)to Lp(R^n×R^m)with p smaller than 1.展开更多
To overcome the unboundedness of the half-plane,we use Khinchine’s inequality and atom decomposition techniques to provide joint Carleson measure characterizations when the difference of composition operators is boun...To overcome the unboundedness of the half-plane,we use Khinchine’s inequality and atom decomposition techniques to provide joint Carleson measure characterizations when the difference of composition operators is bounded or compact from standard weighted Bergman spaces to Lebesgue spaces over the halfplane for all index choices.For applications,we obtain direct analytic characterizations of the bounded and compact differences of composition operators on such spaces.This paper concludes with a joint Carleson measure characterization when the difference of composition operators is Hilbert-Schmidt.展开更多
基金Sponsored by the National NSFC under grant No.19771063
文摘In this article,atomic decompositions and the duals of some B-valued r.v.se- quence spaces are investigated.The results show that it closely depends on the geometrical properties of the sequence that take values in.
基金Supported by the Xinjiang Training of Innovative Personnel Natural Science Foundation of China(Grant No.2020D01C048)the National Natural Science Foundation of China(Grant No.11861062)。
文摘In 2011,Dekel et al.developed highly geometric Hardy spaces H^(p)(Θ),for the full range 0<p≤1,which are constructed by continuous multi-level ellipsoid coverΘof R^(n) with high anisotropy in the sense that the ellipsoids can change shape rapidly from point to point and from level to level.The authors obtain the finite atomic decomposition characterization of Hardy spaces H^(p)(Θ)and as an application,the authors prove that given an admissible triplet(p,q,l)with 1≤q≤∞,if T is a sublinear operator and uniformly bounded elements of some quasi-Banach space B for maps all(p,q,l)-atoms with q<∞(or all continuous(p,q,l)-atoms with q=∞),then T uniquely extends to a bounded sublinear operator from H^(p)(Θ)to B.These results generalize the known results on the anisotropic Hardy spaces of Bownik et al.
文摘A theory recently developed by the present authors is applied to the study of the effect of elastic energy due to atomic size factor on the transformation behaviour of binary solid solutions. lt is found that elastic interaction energy (EIE), which is a part of the total elastic energy plays a key role in both ordering elastic interaction ordering (EIO) and spinodal decomposition. The present study gives a reasonable explanation to the historical dilemmas, "elastic energy paradox" and "atomic size factor paradox . By solving these confusing problems, the coexistence of ordering (EIO) and decomposition, which has been regarded as impossible by conventional theories. can be well understood. The mechanism is as follows: lowering of elastic energy demands EIO, and such an ordering provides a driving force for spinodal decomposition. Therefore, in alloys with large atomic size factor, spinodal decomposition is preceded and induced by ordering. Ordering and spinodal decomposition are thus closely related processes to each
文摘Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.
基金This work was supported by Australian Government through the Australian Research Councilsupported by the National Natural Science Foundation of China(Grant No.10371069)the Natural Science Foundation of Guangdong Province(Grant No.032038).
基金supported by the project "Smoothness Morrey spaces with variable exponents" approved under the agreement "Projektbezogener Personenaustausch mit Portugal-Acoes Integradas Luso-Alems’/DAAD-CRUP"the Centre for Mathematics of the University of Coimbra (Grant No. UID/MAT/00324/2013)+1 种基金funded by the Portuguese Government through FCT/MEC and co-funded by the European Regional Development Fund through the Partnership Agreement PT2020National Science Center of Poland (Grant No. 2014/15/B/ST1/00164)
文摘We study unboundedness of smoothness Morrey spaces on bounded domains ? ? R^n in terms of growth envelopes. It turns out that in this situation the growth envelope function is finite—in contrast to the results obtained by Haroske et al.(2016) for corresponding spaces defined on R^n. A similar effect was already observed by Haroske et al.(2017), where classical Morrey spaces M_(u,p)(?) were investigated. We deal with all cases where the concept is reasonable and also include the tricky limiting cases. Our results can be reformulated in terms of optimal embeddings into the scale of Lorentz spaces L_(p,q)(?).
基金supported in part by the National Natural Science Foundation of China(Grant No.11761026,11761027)Natural Science Foundation of Guangxi(Grant No.2020GXNSFAA159085).
文摘We introduce the variable integral and the smooth exponent Besov spaces associated to non-negative self-adjoint operators.Then we give the equivalent norms via the Peetre type maximal functions and atomic decomposition of these spaces.
基金supported in part by the National Natural Science Foundation of China(Grant Nos.11901495,11771345)the Hunan Provincial Natural Science Foundation(2019JJ50573)the Hunan Education Department Project(18C0109).
文摘Suppose that g(f)are bi-parameter Littlewood-Paley square functions which were introduced by H.Martikainen.It is known that the L^2(R^n×R^m)boundedness and the H1(R^n×R^m)-L1(R^n×R^m)boundedness of g(f)have been proved by H.Martikainen and by Z.Li and Q.Xue,respectively.In this paper,we apply the vector-valued theory,the atomic decomposition of product Hardy spaces,and Journe’s covering lemma to show that g(f)are bounded from H^p(R^n×R^m)to Lp(R^n×R^m)with p smaller than 1.
基金supported by National Natural Science Foundation of China(Grant Nos.11771340 and 11431011)。
文摘To overcome the unboundedness of the half-plane,we use Khinchine’s inequality and atom decomposition techniques to provide joint Carleson measure characterizations when the difference of composition operators is bounded or compact from standard weighted Bergman spaces to Lebesgue spaces over the halfplane for all index choices.For applications,we obtain direct analytic characterizations of the bounded and compact differences of composition operators on such spaces.This paper concludes with a joint Carleson measure characterization when the difference of composition operators is Hilbert-Schmidt.
