In this paper,we study a boundedness property of the Adams type for multilinear fractional integral operators with the multilinear L^(r′,α)-Hörmander condition and their commutators with vector valued BMO funct...In this paper,we study a boundedness property of the Adams type for multilinear fractional integral operators with the multilinear L^(r′,α)-Hörmander condition and their commutators with vector valued BMO functions on a Morrey space and a predual Morrey space.Moreover,we give an endpoint estimate for multilinear fractional integral operators.As an application,we obtain the boundedness of multilinear Fourier multipliers with limited Sobolev regularity on a Morrey space.展开更多
In this note, we consider stochastic heat equation with general additive Gaussian noise. Our aim is to derive some necessary and sufficient conditions on the Gaussian noise in order to solve the corresponding heat equ...In this note, we consider stochastic heat equation with general additive Gaussian noise. Our aim is to derive some necessary and sufficient conditions on the Gaussian noise in order to solve the corresponding heat equation. We investigate this problem invoking two differen t met hods, respectively, based on variance compu tations and on pat h-wise considerations in Besov spaces. We are going to see that, as anticipated, both approaches lead to the same necessary and sufficient condition on the noise. In addition, the path-wise approach brings out regularity results for the solution.展开更多
基金supported by National Natural Science Foundation of China(11871452,12071473)the Beijing Information Science and Technology University Foundation(2025031)。
文摘In this paper,we study a boundedness property of the Adams type for multilinear fractional integral operators with the multilinear L^(r′,α)-Hörmander condition and their commutators with vector valued BMO functions on a Morrey space and a predual Morrey space.Moreover,we give an endpoint estimate for multilinear fractional integral operators.As an application,we obtain the boundedness of multilinear Fourier multipliers with limited Sobolev regularity on a Morrey space.
基金supported by an NSERC granta startup fund of University of Albertasupported by the NSF grant DMS1613163
文摘In this note, we consider stochastic heat equation with general additive Gaussian noise. Our aim is to derive some necessary and sufficient conditions on the Gaussian noise in order to solve the corresponding heat equation. We investigate this problem invoking two differen t met hods, respectively, based on variance compu tations and on pat h-wise considerations in Besov spaces. We are going to see that, as anticipated, both approaches lead to the same necessary and sufficient condition on the noise. In addition, the path-wise approach brings out regularity results for the solution.
