Almost everything you need to know about relatively compact sets in variable Lebesgue spaces

作者：Gorka Przemyslaw^*; Macios Anna

来源：Journal of Functional Analysis, 2015, 269(7): 1925-1949.

DOI：10.1016/j.jfa.2015.06.024

• Compact embedding
• Lebesgue spaces with variable exponents
• Metric measure spaces
• Riesz-Kolmogorov theorem

We study relatively compact sets in variable Lebesgue spaces. The full characterization of such sets is given in the case of variable Lebesgue space on metric measure spaces. The paper contains a detailed discussion of relatively compact sets in variable Lebesgue space on the Euclidean space. Moreover, some applications of the theorems are given.

• 出版日期2015-10-1