SOBOLEV INEQUALITIES FOR RIESZ POTENTIALS OF FUNCTIONS IN OVER NONDOUBLING MEASURE SPACES

Our aim in this paper is to deal with Sobolev inequalities for Riesz potentials of functions in Lebesgue spaces of variable exponents near Sobolev’s exponent over nondoubling metric measure spaces.

Sobolev Embeddings for Generalized Riesz Potentials of Functions in Morrey Spaces over Nondoubling Measure Spaces

Our aim in this paper is to deal with the Sobolev embeddings for generalized Riesz potentials of functions in Morrey spaces over nondoubling measure spaces.

Marcinkiewicz Commutators with Lipschitz Functions in Non-homogeneous Spaces

Under the assumption that μ is a nondoubling measure, we study certain commutators generated by the Lipschitz function and the Marcinkiewicz integral whose kernel satisfies a Hörmander type condition. We establish the boundedness of these commutators on the Lebesgue spaces, Lipschitz spaces, and Hardy spaces. Our results are extensions of known theorems in the doubling case.

A note on Muckenhoupt type weight classes on nondoubling measure spaces

We consider some Muckenhoupt type weight classes on nondoubling measure space (, μ) and give an example of measure μ such that where α 1 ≠ α 2.