As we know,thus far,there has appeared no definition of bilinear spectral multipliers on Heisenberg groups.In this article,we present one reasonable definition of bilinear spectral multipliers on Heisenberg groups and...As we know,thus far,there has appeared no definition of bilinear spectral multipliers on Heisenberg groups.In this article,we present one reasonable definition of bilinear spectral multipliers on Heisenberg groups and investigate its boundedness.We find some restrained conditions to separately ensure its boundedness from C0(H^(n))×L^(2)(H^(n))to L^(2)(H^(n)),from L2(H^(n))×C0(H^(n))to L^(2)(H^(n)),and from L^(p)×L^(q) to L^(r) with 2<p,q<∞,2≤r≤∞.展开更多
We consider Hardy spaces with variable exponents defined by grand maximal function on the Heisenberg group. Then we introduce some equivalent characterizations of variable Hardy spaces. By using atomic decomposition a...We consider Hardy spaces with variable exponents defined by grand maximal function on the Heisenberg group. Then we introduce some equivalent characterizations of variable Hardy spaces. By using atomic decomposition and molecular decomposition we get the boundedness of singular integral operators on variable Hardy spaces. We investigate the Littlewood-Paley characterization by virtue of the boundedness of singular integral operators.展开更多
In this paper, we define the localization operator associated with the spherical mean operator, and show that the localization operator is not only bounded, but also in Schatten-Von Neumann class. We also give a trace...In this paper, we define the localization operator associated with the spherical mean operator, and show that the localization operator is not only bounded, but also in Schatten-Von Neumann class. We also give a trace formula when the symbol function is a nonnegative function.展开更多
In this paper,we give four kinds of sharp estimates of two variants of bilinear Hausdorff operators on stratified groups,involving weighted Lebesgue spaces,classical Morrey spaces and central Morrey spaces.Meanwhile,s...In this paper,we give four kinds of sharp estimates of two variants of bilinear Hausdorff operators on stratified groups,involving weighted Lebesgue spaces,classical Morrey spaces and central Morrey spaces.Meanwhile,some necessary and sufficient conditions of boundness are obtained.展开更多
基金Supported by National Natural Science Foundation of China(11471040 and 11761131002)。
文摘As we know,thus far,there has appeared no definition of bilinear spectral multipliers on Heisenberg groups.In this article,we present one reasonable definition of bilinear spectral multipliers on Heisenberg groups and investigate its boundedness.We find some restrained conditions to separately ensure its boundedness from C0(H^(n))×L^(2)(H^(n))to L^(2)(H^(n)),from L2(H^(n))×C0(H^(n))to L^(2)(H^(n)),and from L^(p)×L^(q) to L^(r) with 2<p,q<∞,2≤r≤∞.
文摘We consider Hardy spaces with variable exponents defined by grand maximal function on the Heisenberg group. Then we introduce some equivalent characterizations of variable Hardy spaces. By using atomic decomposition and molecular decomposition we get the boundedness of singular integral operators on variable Hardy spaces. We investigate the Littlewood-Paley characterization by virtue of the boundedness of singular integral operators.
文摘In this paper, we define the localization operator associated with the spherical mean operator, and show that the localization operator is not only bounded, but also in Schatten-Von Neumann class. We also give a trace formula when the symbol function is a nonnegative function.
基金supported by National Natural Science Foundation of China(Grant Nos.11471040 and 11761131002).
文摘In this paper,we give four kinds of sharp estimates of two variants of bilinear Hausdorff operators on stratified groups,involving weighted Lebesgue spaces,classical Morrey spaces and central Morrey spaces.Meanwhile,some necessary and sufficient conditions of boundness are obtained.
