本文研究了一类带Hardy项和Sobolev临界指数的椭圆型方程。通过变分法,我们得到了方程的能量泛函在零点附近存在局部极小值点,且该极小值点为方程的正解。此外,当方程的扰动项趋于零时,该正解也趋于零。The elliptical equation with Ha...本文研究了一类带Hardy项和Sobolev临界指数的椭圆型方程。通过变分法,我们得到了方程的能量泛函在零点附近存在局部极小值点,且该极小值点为方程的正解。此外,当方程的扰动项趋于零时,该正解也趋于零。The elliptical equation with Hardy terms and Sobolev critical exponents is studied. By the variational methods, we have obtained that there exists a local minimum point of the energy functional related to the equation which is near zero, and the local minimum point is a positive solution of this equation. Moreover, this positive solution tends to zero when the perturbed term goes to zero.展开更多
In this article,we investigate the(big) Hankel operator H_(f) on the Hardy spaces of bounded strongly pseudoconvex domains Ω in C^(n).We observe that H_(f ) is bounded on H~p(Ω)(1 <p <∞) if f belongs to BMO a...In this article,we investigate the(big) Hankel operator H_(f) on the Hardy spaces of bounded strongly pseudoconvex domains Ω in C^(n).We observe that H_(f ) is bounded on H~p(Ω)(1 <p <∞) if f belongs to BMO and we obtain some characterizations for Hf on H^(2)(Ω) of other pseudoconvex domains.In these arguments,Amar's L^(p)-estimations and Berndtsson's L^(2)-estimations for solutions of the ■_(b)-equation play a crucial role.In addition,we solve Gleason's problem for Hardy spaces H^(p)(Ω)(1 ≤p≤∞) of bounded strongly pseudoconvex domains.展开更多
Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying som...Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying some mild assumptions.Let HX,L(ℝ^(n))be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by L.In this article,the authors establish various maximal function characterizations of the Hardy space HX,L(ℝ^(n))and then apply these characterizations to obtain the solvability of the related Cauchy problem.These results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey space.Moreover,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new.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
In this paper,we introduce the weighted multilinear p-adic Hardy operator and weighted multilinear p-adic Ces`aro operator,we also obtain the boundedness of these two operators on the product of p-adic Herz spaces and...In this paper,we introduce the weighted multilinear p-adic Hardy operator and weighted multilinear p-adic Ces`aro operator,we also obtain the boundedness of these two operators on the product of p-adic Herz spaces and p-adic Morrey-Herz spaces,the corresponding operator norms are also established in each case.Moreover,the boundedness of commutators of these two operators with symbols in central bounded mean oscillation spaces and Lipschitz spaces on p-adic Morrey-Herz spaces are also given.展开更多
Letμbe a positive Borel measure on the interval[0,1).The Hankel matrixHμ=(μn,k)n,k≥0 with entries μn,k=μn+k,whereμn=∫[0,1)tndμ(t),induces formally the operator asDHμ(f)(z)=∞∑n=0(∞∑k=0 μn,kak)z^(n),z∈D,...Letμbe a positive Borel measure on the interval[0,1).The Hankel matrixHμ=(μn,k)n,k≥0 with entries μn,k=μn+k,whereμn=∫[0,1)tndμ(t),induces formally the operator asDHμ(f)(z)=∞∑n=0(∞∑k=0 μn,kak)z^(n),z∈D,where f(z)=∞∑n=0a_(n)z^(n) is an analytic function in D.We characterize the positive Borel measures on[0,1)such thatDHμ(f)(z)=f[0,1)f(t)/(1-tz)^(2)dμ(t) for all f in the Hardy spaces Hp(0<p<∞),and among these we describe those for which is a bounded(resp.,compact)operator from Hp(0<p<∞)into Hq(q>p and q≥1).We also study the analogous problem in the Hardy spaces H^(p)(1≤p≤2).展开更多
This paper deals with a general class of weighted multilinear Hardy-Cesaro op- erators that acts on the product of Lebesgue spaces and central Morrey spaces. Their sharp bounds are also obtained. In addition, we obtai...This paper deals with a general class of weighted multilinear Hardy-Cesaro op- erators that acts on the product of Lebesgue spaces and central Morrey spaces. Their sharp bounds are also obtained. In addition, we obtain sufficient and necessary conditions on weight functions so that the commutators of these weighted multilinear Hardy-Cesaro oper- ators （with symbols in central BMO spaces） are bounded on the product of central Morrey spaces. These results extends known results on multilinear Hardy operators.展开更多
文摘本文研究了一类带Hardy项和Sobolev临界指数的椭圆型方程。通过变分法,我们得到了方程的能量泛函在零点附近存在局部极小值点,且该极小值点为方程的正解。此外,当方程的扰动项趋于零时,该正解也趋于零。The elliptical equation with Hardy terms and Sobolev critical exponents is studied. By the variational methods, we have obtained that there exists a local minimum point of the energy functional related to the equation which is near zero, and the local minimum point is a positive solution of this equation. Moreover, this positive solution tends to zero when the perturbed term goes to zero.
基金supported by the National Natural Science Foundation of China(12271101)。
文摘In this article,we investigate the(big) Hankel operator H_(f) on the Hardy spaces of bounded strongly pseudoconvex domains Ω in C^(n).We observe that H_(f ) is bounded on H~p(Ω)(1 <p <∞) if f belongs to BMO and we obtain some characterizations for Hf on H^(2)(Ω) of other pseudoconvex domains.In these arguments,Amar's L^(p)-estimations and Berndtsson's L^(2)-estimations for solutions of the ■_(b)-equation play a crucial role.In addition,we solve Gleason's problem for Hardy spaces H^(p)(Ω)(1 ≤p≤∞) of bounded strongly pseudoconvex domains.
基金supported by the National Key Research and Development Program of China(2020YFA0712900)the National Natural Science Foundation of China(12371093,12071197,12122102 and 12071431)+2 种基金the Key Project of Gansu Provincial National Science Foundation(23JRRA1022)the Fundamental Research Funds for the Central Universities(2233300008 and lzujbky-2021-ey18)the Innovative Groups of Basic Research in Gansu Province(22JR5RA391).
文摘Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying some mild assumptions.Let HX,L(ℝ^(n))be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by L.In this article,the authors establish various maximal function characterizations of the Hardy space HX,L(ℝ^(n))and then apply these characterizations to obtain the solvability of the related Cauchy problem.These results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey space.Moreover,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new.
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.
文摘In this paper,we introduce the weighted multilinear p-adic Hardy operator and weighted multilinear p-adic Ces`aro operator,we also obtain the boundedness of these two operators on the product of p-adic Herz spaces and p-adic Morrey-Herz spaces,the corresponding operator norms are also established in each case.Moreover,the boundedness of commutators of these two operators with symbols in central bounded mean oscillation spaces and Lipschitz spaces on p-adic Morrey-Herz spaces are also given.
基金supported by the Zhejiang Provincial Natural Science Foundation (LY23A010003)the National Natural Science Foundation of China (11671357).
文摘Letμbe a positive Borel measure on the interval[0,1).The Hankel matrixHμ=(μn,k)n,k≥0 with entries μn,k=μn+k,whereμn=∫[0,1)tndμ(t),induces formally the operator asDHμ(f)(z)=∞∑n=0(∞∑k=0 μn,kak)z^(n),z∈D,where f(z)=∞∑n=0a_(n)z^(n) is an analytic function in D.We characterize the positive Borel measures on[0,1)such thatDHμ(f)(z)=f[0,1)f(t)/(1-tz)^(2)dμ(t) for all f in the Hardy spaces Hp(0<p<∞),and among these we describe those for which is a bounded(resp.,compact)operator from Hp(0<p<∞)into Hq(q>p and q≥1).We also study the analogous problem in the Hardy spaces H^(p)(1≤p≤2).
基金supported by Vietnam National Foundation for Science and Technology Development(101.02-2014.51)
文摘This paper deals with a general class of weighted multilinear Hardy-Cesaro op- erators that acts on the product of Lebesgue spaces and central Morrey spaces. Their sharp bounds are also obtained. In addition, we obtain sufficient and necessary conditions on weight functions so that the commutators of these weighted multilinear Hardy-Cesaro oper- ators （with symbols in central BMO spaces） are bounded on the product of central Morrey spaces. These results extends known results on multilinear Hardy operators.
