Generalized Morrey spaces and trace operator

Abstract

The theory of generalized Besov-Morrey spaces and generalized Triebel-Lizorkin-Morrey spaces is developed. Generalized Morrey spaces, which T. Mizuhara and E. Nakai proposed, are equipped with a parameter and a function. The trace property is one of the main focuses of the present paper, which will clarify the role of the parameter of generalized Morrey spaces. The quarkonial decomposition is obtained as an application of atomic decomposition. In the end, the relation between the function spaces dealt in the present paper and the foregoing researches is discussed.

61 pages, Published as Shohei Nakamura, Takahiro Noi and Yoshihiro Sawano, Generalized Morrey spaces and trace operator. Sci. China Math. 59 (2016), no. 2, 281-336

References in corpus (5)

• Interpolation of Morrey-Campanato and Related Smoothness Spaces
• Generalized coorbit space theory and inhomogeneous function spaces of Besov-Lizorkin-Triebel type
• Equivalent boundedness of Marcinkiewicz integrals on non-homogeneous metric measure spaces
• Hardy spaces $H^p$ over non-homogeneous metric measure spaces and their applications
• $L^{\infty }$ estimates and integrability by compensation in Besov-Morrey spaces and applications

Cited by in corpus (2)

• Homogeneous Besov spaces
• Decompositions with atoms and molecules for variable exponent Triebel-Lizorkin-Morrey spaces