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Morrey spaces and fractional integral operators |
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| Authors: | A Eridani Vakhtang Kokilashvili Alexander Meskhi |
| Institution: | aDepartment of Mathematics, Airlangga University, Campus C, Mulyorejo, Surabaya 60115, Indonesia;bSchool of Mathematical Sciences, Government College University, 68-B New Muslim Town, Lahore, Pakistan;cA. Razmadze Mathematical Institute, M. Aleksidze St., Tbilisi 0193, Georgia |
| Abstract: | The present paper is devoted to the boundedness of fractional integral operators in Morrey spaces defined on quasimetric measure spaces. In particular, Sobolev, trace and weighted inequalities with power weights for potential operators are established. In the case when measure satisfies the doubling condition the derived conditions are simultaneously necessary and sufficient for appropriate inequalities. |
| Keywords: | Fractional integrals Morrey spaces Non-homogeneous spaces Trace inequality Two-weight inequality |
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