Equiconvergence theorems for Laguerre series
The Szegö equiconvergence theorem for the Laguerre series is improved. In particular, a system of exact sufficient conditions is given.
Optimal embeddings of generalized homogeneous Sobolev spaces
We prove optimal embeddings of homogeneous Sobolev spaces built over function spaces in ℝⁿ with K-monotone and rearrangement invariant norm into other rearrangement invariant function spaces. The investigation is based on pointwise and integral estimates of the rearrangement or the oscillation of the rearrangement of f in terms of the rearrangement of the derivatives of f.
Metastability in the shadow system for Gierer-Meinhardt's equations.
Sharp estimates of the embedding constants for Besov spaces.
Sharp estimates are obtained for the rates of blow up of the norms of embeddings of Besov spaces in Lorentz spaces as the parameters approach critical values.
On the dependence of parameters in the equivalence theorem for the real method
We determine the exact dependence on of the constants in the equivalence theorem for the real interpolation method with pairs of -normed spaces.
Local stability of spike steady states in a simplified Gierer-Meinhardt system.
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