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On generalized Bergman spaces

Wolfgang Lusky (1996)

Studia Mathematica

Let D be the open unit disc and μ a positive bounded measure on [0,1]. Extending results of Mateljević/Pavlović and Shields/Williams we give Banach-space descriptions of the classes of all harmonic (holomorphic) functions f: D → ℂ satisfying ʃ 0 1 ( ʃ 0 2 π | f ( r e i φ ) | p d φ ) q / p d μ ( r ) < .

On generalized Moser-Trudinger inequalities without boundary condition

Robert Černý (2012)

Czechoslovak Mathematical Journal

We give a version of the Moser-Trudinger inequality without boundary condition for Orlicz-Sobolev spaces embedded into exponential and multiple exponential spaces. We also derive the Concentration-Compactness Alternative for this inequality. As an application of our Concentration-Compactness Alternative we prove that a functional with the sub-critical growth attains its maximum.

On imbedding theorems for weighted anisotropic Sobolev spaces

Wojciech M. Zajączkowski (2002)

Applicationes Mathematicae

Using the Il'in integral representation of functions, imbedding theorems for weighted anisotropic Sobolev spaces in 𝔼ⁿ are proved. By the weight we assume a power function of the distance from an (n-2)-dimensional subspace passing through the domain considered.

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