Alois Kufner
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New equivalent conditions for Hardy-type inequalities Open
We consider a Hardy-type inequality with Oinarov's kernel in weighted Lebesgue spaces. We give new equivalent conditions for satisfying the inequality, and provide lower and upper estimates for its best constant. The findings are crucial i…
On weighted Fourier inequalities - some new scales of equivalent conditions Open
For Lebesgue spaces on Rn, we study two-weight p → q-inequalities for Fourier\ntransform. Some sufficient conditions on weights for such inequalities are known for special\nranges of parameters p and q. In the same ranges of parameters we …
Higher Order Hardy Inequalities Open
This note deals with the inequalitymore precisely, with conditions on the parameters p > 1, q > 0 and on the weight functions w 0 , w k (measurable and positive almost everywhere) which ensure that (1) holds for all functions u from a cert…
Hardy inequality, compact embeddings and properties of certain eigenvalue problems Open
We point out the connection between the Hardy inequality,\ncompact embedding of weighted function spaces and the properties of\nthe spectra of certain eigenvalue problems. Necessary and sufficient\nconditions in terms of the Muckenhoupt fu…
Hardy type inequalities with kernels: The current status and some new results Open
We consider the general Hardy type operator where is a positive and measurable kernel. To characterize the weights u and v so that is still an open problem for any parameters p and q . However, for special cases the solution is known for s…