Norm inequalities in some subspaces of Morrey space
We give norm inequalities for some classical operators in amalgam spaces and in some subspaces of Morrey space.
We give norm inequalities for some classical operators in amalgam spaces and in some subspaces of Morrey space.
We study the duality theory of the weighted multi-parameter Triebel-Lizorkin spaces . This space has been introduced and the result for has been proved in Ding, Zhu (2017). In this paper, for , we establish its dual space .
Let and , where a(s) is a positive continuous function such that and b(s) is quasi-increasing and . Then the following statements for the Hardy-Littlewood maximal function Mf(x) are equivalent: (j) there exist positive constants and such that for all ; (jj) there exist positive constants and such that for all .
We establish a decomposition of non-negative Radon measures on which extends that obtained by Strichartz [6] in the setting of -dimensional measures. As consequences, we deduce some well-known properties concerning the density of non-negative Radon measures. Furthermore, some properties of non-negative Radon measures having their Riesz potential in a Lebesgue space are obtained.
The Hardy inequality with holds for if is an open set with a sufficiently smooth boundary and if . P. Hajlasz proved the pointwise counterpart to this inequality involving a maximal function of Hardy-Littlewood type on the right hand side and, as a consequence, obtained the integral Hardy inequality. We extend these results for gradients of higher order and also for .
In their celebrated paper [3], Burkholder, Gundy, and Silverstein used Brownian motion to derive a maximal function characterization of spaces for 0 < p < ∞. In the present paper, we show that the methods in [3] extend to higher dimensions and yield a dimension-free weak type (1,1) estimate for a conjugate function on the N-dimensional torus.
It is known that the weak type (1,1) for the Hardy-Littlewood maximal operator can be obtained from the weak type (1,1) over Dirac deltas. This theorem is due to M. de Guzmán. In this paper, we develop a technique that allows us to prove such a theorem for operators and measure spaces in which Guzmán's technique cannot be used.
In this paper we give a sufficient condition on the pair of weights for the boundedness of the Weyl fractional integral from into . Under some restrictions on and , this condition is also necessary. Besides, it allows us to show that for any there exist non-trivial weights such that is bounded from into itself, even in the case .