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

• Main Authors: Hendra Gunawan, Denny Ivanal Hakim, Yoshihiro Sawano, Idha Sihwaningrum
• Format: Article
• Language: English
• Published: Hindawi Limited 2013-01-01
• Series: Journal of Function Spaces and Applications
• Online Access: http://dx.doi.org/10.1155/2013/809704

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.