For a family of smooth functions defined in multi-dimensional space,we show that,under certain generic conditions,all minimal and maximal points are non-degenerate.
We continue our investigations on pointwise multipliers for Besov spaces of dominating mixed smoothness. This time we study the algebra property of the classes S_(p,q)~rB(R^d) with respect to pointwise multiplication....We continue our investigations on pointwise multipliers for Besov spaces of dominating mixed smoothness. This time we study the algebra property of the classes S_(p,q)~rB(R^d) with respect to pointwise multiplication. In addition, if p≤q, we are able to describe the space of all pointwise multipliers for S_(p,q)~rB(R^d).展开更多
For a family of smooth functions, the author shows that, under certain generic conditions, all extremal(minimal and maximal) points are non-degenerate.
Inspired by Durfee Conjecture in singularity theory, Yau formulated the Yau number theoretic conjecture(see Conjecture 1.3) which gives a sharp polynomial upper bound of the number of positive integral points in an n-...Inspired by Durfee Conjecture in singularity theory, Yau formulated the Yau number theoretic conjecture(see Conjecture 1.3) which gives a sharp polynomial upper bound of the number of positive integral points in an n-dimensional(n≥3) polyhedron. It is well known that getting the estimate of integral points in the polyhedron is equivalent to getting the estimate of the de Bruijn function ψ(x, y), which is important and has a number of applications to analytic number theory and cryptography. We prove the Yau number theoretic conjecture for n = 6. As an application, we give a sharper estimate of function ψ(x, y) for 5≤y < 17, compared with the result obtained by Ennola.展开更多
In this paper, by sharp function estimates and certain weak type endpoint estimates, the authors establish some weighted norm inequalities with Ap weights for the multilinear singular integral operators with non-smoot...In this paper, by sharp function estimates and certain weak type endpoint estimates, the authors establish some weighted norm inequalities with Ap weights for the multilinear singular integral operators with non-smooth kernels.展开更多
基金supported by National Basic Research Program of China(973 Program)(Grant No.2013CB834100)National Natural Science Foundation of China(Grant Nos.11171146 and 11201222)the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘For a family of smooth functions defined in multi-dimensional space,we show that,under certain generic conditions,all minimal and maximal points are non-degenerate.
文摘We continue our investigations on pointwise multipliers for Besov spaces of dominating mixed smoothness. This time we study the algebra property of the classes S_(p,q)~rB(R^d) with respect to pointwise multiplication. In addition, if p≤q, we are able to describe the space of all pointwise multipliers for S_(p,q)~rB(R^d).
基金supported by the National Natural Science Foundation of China(Nos.11201222,11171146)the Basic Research Program of Jiangsu Province(No.BK2008013)a program of the Priority Academic Program Development of Jiangsu Province
文摘For a family of smooth functions, the author shows that, under certain generic conditions, all extremal(minimal and maximal) points are non-degenerate.
基金the Start-Up Fund from Tsinghua University, Tsinghua University Initiative Scientific Research Program and National Natural Science Foundation of China (Grant No. 11401335)
文摘Inspired by Durfee Conjecture in singularity theory, Yau formulated the Yau number theoretic conjecture(see Conjecture 1.3) which gives a sharp polynomial upper bound of the number of positive integral points in an n-dimensional(n≥3) polyhedron. It is well known that getting the estimate of integral points in the polyhedron is equivalent to getting the estimate of the de Bruijn function ψ(x, y), which is important and has a number of applications to analytic number theory and cryptography. We prove the Yau number theoretic conjecture for n = 6. As an application, we give a sharper estimate of function ψ(x, y) for 5≤y < 17, compared with the result obtained by Ennola.
基金supported by National Natural Science Foundation of China (Grant No. 10971228),supported by National Natural Science Foundation of China (Grant Nos. 10871024, 10931001)
文摘In this paper, by sharp function estimates and certain weak type endpoint estimates, the authors establish some weighted norm inequalities with Ap weights for the multilinear singular integral operators with non-smooth kernels.
