Limit cases of reiteration theorems
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Publication:5174429
DOI10.1002/mana.201300251zbMath1335.46019OpenAlexW1668645065MaRDI QIDQ5174429
Pedro Fernández-Martínez, Teresa Signes
Publication date: 17 February 2015
Published in: Mathematische Nachrichten (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/mana.201300251
Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Interpolation between normed linear spaces (46B70) Rate of growth of functions, orders of infinity, slowly varying functions (26A12)
Related Items (23)
Characterization of interpolation between grand, small or classical Lebesgue spaces ⋮ General reiteration theorems for \(\mathcal{R}\) and \(\mathcal{L}\) classes: mixed interpolation of \(\mathcal{R}\) and \(\mathcal{L}\)-spaces ⋮ New limiting variants of the classical reiteration theorem for the \(K\)-interpolation method ⋮ Limiting reiteration for real interpolation with logarithmic functions ⋮ General Holmstedt's formulae for the \(K\)-functional ⋮ On grand and small Lebesgue and Sobolev spaces and some applications to PDE's ⋮ General reiteration theorems for \(\mathcal{R}\) and \(\mathcal{L}\) classes: case of right \(\mathcal{R}\)-spaces and left \(\mathcal{L}\)-spaces ⋮ Some interpolation formulae for grand and small Lorentz spaces ⋮ Some examples of equivalent rearrangement‐invariant quasi‐norms defined via f∗$f^*$ or f∗∗$f^{**}$ ⋮ Description of K‐spaces by means of J‐spaces and the reverse problem in the limiting real interpolation ⋮ Grand Lebesgue Spaces are really Banach algebras relative to the convolution on unimodular locally compact groups equipped with Haar measure ⋮ Connection between weighted tail, Orlicz, Grand Lorentz and Grand Lebesgue norms ⋮ Holmstedt's formula for the K‐functional: the limit case θ0=θ1$\theta _0=\theta _1$ ⋮ Reiteration formulae for the real interpolation method including \(\mathcal{L}\) or \(\mathcal{R}\) limiting spaces ⋮ General reiteration theorems for \(\mathcal{R}\) and \(\mathcal{L}\) classes: case of left \(\mathcal{R} \)-spaces and right \(\mathcal{L} \)-spaces ⋮ Some reiteration theorems for \(\mathscr{R}\), \(\mathscr{L}\), \(\mathscr{R}\mathscr{R}\), \(\mathscr{R}\mathscr{L}\), \(\mathscr{L}\mathscr{R}\), and \(\mathscr{L}\mathscr{L}\) limiting interpolation spaces ⋮ Reiteration theorems with extreme values of parameters ⋮ Compactness results for a class of limiting interpolation methods ⋮ New Young inequalities and applications ⋮ Reiteration theorem for \(\mathcal{R}\) and \(\mathcal{L}\)-spaces with the same parameter ⋮ A LIMITING CASE OF ULTRASYMMETRIC SPACES ⋮ Unnamed Item ⋮ Function Spaces of Logarithmic Smoothness: Embeddings and Characterizations
Cites Work
- Real interpolation with logarithmic functors.
- On an extreme class of real interpolation spaces
- On the integrability of the Jacobian under minimal hypotheses
- On embeddings of logarithmic Bessel potential spaces
- Duality and reflexivity in grand Lebesgue spaces
- Grand and small Lebesgue spaces and their analogs
- Optimal Sobolev imbeddings involving rearrangement-invariant quasinorms
- Weak type interpolation near ``endpoint spaces
- Some reiteration formulae for limiting real methods
- Sharp embeddings of Besov-type spaces
- Intermediate spaces and the class L \(log^+ L\)
- Reiteration theorems for the K -interpolation method in limiting cases
- REAL INTERPOLATION WITH SYMMETRIC SPACES AND SLOWLY VARYING FUNCTIONS
- Extrapolation Spaces and Almost-Everywhere Convergence of Singular Integrals
- A function parameter in connection with interpolation of Banach spaces.
- On generalized Lorentz-Zygmund spaces
- ULTRASYMMETRIC SPACES
- Real Interpolation with Logarithmic Functors and Reiteration
- Limiting reiteration for real interpolation with slowly varying functions
- Lorentz–Karamata spaces, Bessel and Riesz potentials and embeddings
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