On embeddings and traces in Sobolev spaces with weights of power type
The project DML-CZ: The Czech Digital Mathematics Library has been implemented since 2005 and in 2010 switched over to routine operation. This report describes progress, growth and usage of the DML-CZ, the experience from cooperation with content providers in the designed editorial workflow, some newly implemented features, adjustments of the workflow following from both the ongoing practical experience and the requirements of the advancing EuDML project, the general public acceptance and attendance...
We give conditions on pairs of weights which are necessary and sufficient for the operator to be a weak type mapping of one weighted Lorentz space in another one. The kernel is an anisotropic radial decreasing function.
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 .
Experience in setting up a workflow from scanned images of mathematical papers into a fully fledged mathematical library is described on the example of the project Czech Digital Mathematics Library DML-CZ. An overview of the whole process is given, with description of all main production steps. DML-CZ has recently been launched to public with more than 100,000 digitized pages.
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