Geodesic
Embedding theorems for weighted classes of harmonic and analytic functions
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part V, Tome 47 (1974), pp. 120-137

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The inequality \[ (\int_\Omega|u|^qd\mu)^{1/q} \leq C (\int_\Omega|u|^p\rho d\lambda)^{1/p}, \tag{1} \] is established for analytic (harmonic) functions. Here $\rho$ is a continuous weight functions, $\lambda$ the Lebesgue measure and $\mu$ – a Borel measure. Necessary and sufficient conditions on the measure $\mu$ are given for some concrete $\Omega$ and $\rho$. 
@article{ZNSL_1974_47_a7,
     author = {V. L. Oleinik},
     title = {Embedding theorems for weighted classes of harmonic and analytic functions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {120--137},
     publisher = {mathdoc},
     volume = {47},
     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1974_47_a7/}
}
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V. L. Oleinik. Embedding theorems for weighted classes of harmonic and analytic functions. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part V, Tome 47 (1974), pp. 120-137. http://geodesic.mathdoc.fr/item/ZNSL_1974_47_a7/