Optimality problems in Orlicz spaces

DOI10.1016/j.aim.2023.109273arXiv2209.14208MaRDI QIDQ6049892

Luboš Pick, Jakub Takáč, Vít Musil

Publication date: 11 October 2023

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2209.14208

zbMATH Keywords

Laplace transformmaximal operatoroptimalityOrlicz spacerearrangement-invariant spaceSobolev embedding

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Maximal functions, Littlewood-Paley theory (42B25)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Optimal rearrangement invariant Sobolev embeddings in mixed norm spaces
• Optimal Sobolev type inequalities in Lorentz spaces
• Optimal extension of Fourier multiplier operators in \(L^p(G)\)
• Absolutely continuous embeddings of rearrangement-invariant spaces
• Lebesgue and Sobolev spaces with variable exponents
• Optimal limiting embeddings for \(\Delta\)-reduced Sobolev spaces in \(L^1\)
• Editor's note: the differentiability of functions in \({\mathbb{R}}^ n\)
• Optimal Calderón spaces for generalized Bessel potentials
• Linear operators, Fourier integral operators and \(k\)-plane transforms on rearrangement-invariant quasi-Banach function spaces
• Optimal Gaussian Sobolev embeddings
• A sharp inequality of J. Moser for higher order derivatives
• Best constant in Sobolev inequality
• A proof of a logarithmic Sobolev inequality
• Sobolev embeddings into spaces of Campanato, Morrey, and Hölder type
• Sobolev embeddings into BMO, VMO, and \(L_{\infty}\)
• Sharp regularity estimates for quasi-linear elliptic dead core problems and applications
• Sharp Sobolev type embeddings on the entire Euclidean space
• Optimal function spaces for the Laplace transform
• Optimal Orlicz-Sobolev embeddings
• Improving sharp Sobolev type inequalities by optimal remainder gradient norms
• Optimal Sobolev imbeddings involving rearrangement-invariant quasinorms
• Weak type interpolation near ``endpoint spaces
• Optimal local embeddings of Besov spaces involving only slowly varying smoothness
• Symmetric gradient Sobolev spaces endowed with rearrangement-invariant norms
• Wiener-Luxemburg amalgam spaces
• Sharp Sobolev inequalities in Lorentz spaces for a mean oscillation
• Higher-order Sobolev embeddings and isoperimetric inequalities
• Boundedness of classical operators on rearrangement-invariant spaces
• Sobolev embeddings, rearrangement-invariant spaces and Frostman measures
• Optimal extension of the Fourier transform and convolution operator on compact groups
• Sobolev embeddings in Orlicz and Lorentz spaces with measures
• Fractional maximal operator in Orlicz spaces
• Optimal Sobolev embeddings on \(\mathbb R^n\)
• Espaces d'interpolation et théorème de Soboleff
• Convolution operators and L(p, q) spaces
• On L(p,q) spaces
• Indices for the Orlicz spaces
• Fractional Orlicz-Sobolev embeddings
• Optimal Sobolev trace embeddings
• Pointwise multipliers of Calderón-Lozanovskiǐ spaces
• Almost-compact embeddings
• On Hardy - Littlewood Maximal Functions in Orlicz Spaces
• Higher-order Sobolev and Poincaré inequalities in Orlicz spaces
• Optimal Sobolev imbeddings
• Fine behavior of functions whose gradients are in an Orlicz space
• Function Spaces Continuously Paired by Operators of Convolution-Type
• Imbedding theorems of Sobolev type in potential theory.
• A note on limiting cases of sobolev embeddings and convolution inequalities
• Logarithmic Sobolev Inequalities
• On generalized Lorentz-Zygmund spaces
• A sharp embedding theorem for Orlicz-Sobolev spaces
• Embeddings of homogeneous Sobolev spaces on the entire space
• Optimal domain spaces in Orlicz-Sobolev embeddings
• Optimal Embeddings of Calderón Spaces in Hölder-Zygmund Spaces
• Weak*-sequential closure and the characteristic of subspaces of conjugate Banach spaces
• Intermediate spaces and interpolation, the complex method
• On the sharpness of a limiting case of the Sobolev imbedding theorem
• Inequalities for Fourier transforms
• Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data: The subcritical case
• Sobolev Spaces
• On the set of values of a finite measure
• Function Spaces
• A fully anisotropic Sobolev inequality
• Orlicz-Sobolev boundary trace embeddings
• Optimal Orlicz domains in Sobolev embeddings into Marcinkiewicz spaces