The generalized stability of the Euler-Lagrange quadratic mappings in the framework of non-Archimedean random normed spaces is proved. The interdisciplinary relation among the theory of random spaces, the theory of no...The generalized stability of the Euler-Lagrange quadratic mappings in the framework of non-Archimedean random normed spaces is proved. The interdisciplinary relation among the theory of random spaces, the theory of non-Archimedean spaces, and the theory of functional equations is presented.展开更多
In this paper, the boundedness of commutators generated by the n- dimensional fractional Hardy operators and Lipschitz functions on p-adic function spaces are obtained. The authors show that these commutators are boun...In this paper, the boundedness of commutators generated by the n- dimensional fractional Hardy operators and Lipschitz functions on p-adic function spaces are obtained. The authors show that these commutators are bounded on Herz space and Lebesgue space with suitable indexes. Moreover, the commutator of Hardy- Littlewood-Poly~ operator is also considered.展开更多
The convergence of linear fractional transformations is an important topic in mathematics.We study the pointwise convergence of p-adic Mbius maps,and classify the possibilities of limits of pointwise convergent sequen...The convergence of linear fractional transformations is an important topic in mathematics.We study the pointwise convergence of p-adic Mbius maps,and classify the possibilities of limits of pointwise convergent sequences of Mbius maps acting on the projective line P1(C p),where C p is the completion of the algebraic closure of Q p.We show that if the set of pointwise convergence of a sequence of p-adic Mbius maps contains at least three points,the sequence of p-adic Mbius maps either converges to a p-adic Mbius map on the projective line P1(C p),or converges to a constant on the set of pointwise convergence with one unique exceptional point.This result generalizes the result of Piranian and Thron(1957)to the non-archimedean settings.展开更多
In this paper we get the sharp estimates of the p-adic Hardy and Hard^Littlewood-Pdlya operators on L^q （｜x｜apdx）. Also, we prove that the commutators generated by the p-adic Hardy operators （Hardy-Littlewood-Pdl...In this paper we get the sharp estimates of the p-adic Hardy and Hard^Littlewood-Pdlya operators on L^q （｜x｜apdx）. Also, we prove that the commutators generated by the p-adic Hardy operators （Hardy-Littlewood-Pdlya operators） and the central BMO functions are bounded on L^q （｜x｜apdx）, more generally, on Herz spaces.展开更多
基金supported by the Natural Science Foundation of Yibin University(No.2009Z03)
文摘The generalized stability of the Euler-Lagrange quadratic mappings in the framework of non-Archimedean random normed spaces is proved. The interdisciplinary relation among the theory of random spaces, the theory of non-Archimedean spaces, and the theory of functional equations is presented.
基金The NSF(11261055)of Chinathe NSF(2012211B28,2011211A005)of Xinjiangthe Open Foundation Project(2012ZDXK002)of Key Disciplines in Xinjiang
文摘In this paper, the boundedness of commutators generated by the n- dimensional fractional Hardy operators and Lipschitz functions on p-adic function spaces are obtained. The authors show that these commutators are bounded on Herz space and Lebesgue space with suitable indexes. Moreover, the commutator of Hardy- Littlewood-Poly~ operator is also considered.
基金supported by National Natural Science Foundation of China(Grant Nos.10831004 and 11301510)
文摘The convergence of linear fractional transformations is an important topic in mathematics.We study the pointwise convergence of p-adic Mbius maps,and classify the possibilities of limits of pointwise convergent sequences of Mbius maps acting on the projective line P1(C p),where C p is the completion of the algebraic closure of Q p.We show that if the set of pointwise convergence of a sequence of p-adic Mbius maps contains at least three points,the sequence of p-adic Mbius maps either converges to a p-adic Mbius map on the projective line P1(C p),or converges to a constant on the set of pointwise convergence with one unique exceptional point.This result generalizes the result of Piranian and Thron(1957)to the non-archimedean settings.
基金Supported by National Natural Science Foundation of China(Grant Nos.10901076,10931001,11126203and11171345)Natural Science Foundation of Shandong Province(Grant No.ZR2010AL006)
文摘In this paper we get the sharp estimates of the p-adic Hardy and Hard^Littlewood-Pdlya operators on L^q （｜x｜apdx）. Also, we prove that the commutators generated by the p-adic Hardy operators （Hardy-Littlewood-Pdlya operators） and the central BMO functions are bounded on L^q （｜x｜apdx）, more generally, on Herz spaces.
