Denny Ivanal Hakim

Weak Type Inequalities for Some Integral Operators on Generalized Nonhomogeneous Morrey Spaces

We prove weak type inequalities for some integral operators, especially generalized fractional integral operators, on generalized Morrey spaces of nonhomogeneous type. The inequality for generalized fractional integral operators is proved by using two different techniques: one uses the Chebyshev inequality and some inequalities involving the modified Hardy-Littlewood maximal operator and the other uses a Hedberg type inequality and weak type inequalities for the modified Hardy-Littlewood maximal operator. Our results generalize the weak type inequalities for fractional integral operators on generalized non-homogeneous Morrey spaces and extend to some singular integral operators. In addition, we also prove the boundedness of generalized fractional integral operators on generalized non-homogeneous Orlicz-Morrey spaces.

Complex interpolation of -spaces

Abstract The upper and lower complex interpolation of -spaces and -spaces are considered. When , and u are finite, we prove that . Otherwise, the space is a closed subspace of . We also establish interpolation results of certain closed subspaces of -spaces and -spaces, which are the closure of linear subspaces satisfying the lattice condition.

Complex Interpolation of Morrey Spaces

In this article, we extend the previous results on the complex interpolation of Morrey spaces to the case when \(0<q \le p<\infty \). We show that the space produced by the first complex interpolation functor \([{\mathcal M}^{p_0}_{q_0},{\mathcal M}^{p_1}_{q_1}]_\theta \) is a subset of the Morrey space \({\mathcal M}^p_q\) and it contains some closed subspaces of \({\mathcal M}^p_q\). Meanwhile, we prove that Morrey spaces are closed under the second complex interpolation functor. We also present the complex interpolation of certain closed subspaces of Morrey spaces.