3 results
Trudinger’s inequalities for Riesz potentials in Morrey spaces of double phase functionals on half spaces
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- Journal:
- Canadian Mathematical Bulletin / Volume 65 / Issue 4 / December 2022
- Published online by Cambridge University Press:
- 27 December 2021, pp. 924-935
- Print publication:
- December 2022
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SOBOLEV’S INEQUALITY FOR MUSIELAK–ORLICZ–MORREY SPACES OVER METRIC MEASURE SPACES
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- Journal:
- Journal of the Australian Mathematical Society / Volume 110 / Issue 3 / June 2021
- Published online by Cambridge University Press:
- 02 October 2019, pp. 371-385
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- June 2021
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Our aim in this paper is to establish a generalization of Sobolev’s inequality for Riesz potentials
$J_{\unicode[STIX]{x1D6FC}(\cdot )}^{\unicode[STIX]{x1D70E}}f$ of functions 
$f$ in Musielak–Orlicz–Morrey spaces 
$L^{\unicode[STIX]{x1D6F7},\unicode[STIX]{x1D705}}(X)$. As a corollary we obtain Sobolev’s inequality for double phase functionals with variable exponents.
Sobolev’s Inequality for Riesz Potentials of Functions in Musielak–Orlicz–Morrey Spaces Over Non-doubling Metric Measure Spaces
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- Journal:
- Canadian Mathematical Bulletin / Volume 63 / Issue 2 / June 2020
- Published online by Cambridge University Press:
- 06 September 2019, pp. 287-303
- Print publication:
- June 2020
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Our aim in this paper is to establish a generalization of Sobolev’s inequality for Riesz potentials
$I_{\unicode[STIX]{x1D6FC}(\,\cdot \,),\unicode[STIX]{x1D70F}}f$ of order 
$\unicode[STIX]{x1D6FC}(\,\cdot \,)$ with 
$f\in L^{\unicode[STIX]{x1D6F7},\unicode[STIX]{x1D705},\unicode[STIX]{x1D703}}(X)$ over bounded non-doubling metric measure spaces. As a corollary we obtain Sobolev’s inequality for double phase functionals with variable exponents.
