Zobecněné trigonometrické funkce z různých úhlů pohledu
Alternative characterisations of Lorentz-Karamata spaces
We present new formulae providing equivalent quasi-norms on Lorentz-Karamata spaces. Our results are based on properties of certain averaging operators on the cone of non-negative and non-increasing functions in convenient weighted Lebesgue spaces. We also illustrate connections between our results and mapping properties of such classical operators as the fractional maximal operator and the Riesz potential (and their variants) on the Lorentz-Karamata spaces.
Approximation and entropy numbers of embeddings in weighted Orlicz spaces
Upper estimates are obtained for approximation and entropy numbers of the embeddings of weighted Sobolev spaces into appropriate weighted Orlicz spaces. Results are given when the underlying space domain is bounded and for certain unbounded domains.
On a higher-order Hardy inequality
The Hardy inequality with holds for if is an open set with a sufficiently smooth boundary and if . P. Hajlasz proved the pointwise counterpart to this inequality involving a maximal function of Hardy-Littlewood type on the right hand side and, as a consequence, obtained the integral Hardy inequality. We extend these results for gradients of higher order and also for .
Remarks on inequalities of Poincaré type
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