Characterisation of Embeddings in Lorentz Spaces

DOI10.1017/S0004972700039484zbMath1128.26012OpenAlexW2035586900MaRDI QIDQ5756324

Amiran Gogatishvili, Lars-Erik Persson, Christopher A. Okpoti, Maria Johansson

Publication date: 4 September 2007

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0004972700039484

zbMATH Keywords

discretization methodweight functionsLorentz spacesanti-discretization method

Mathematics Subject Classification ID

Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) (47B37) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (15)

Weighted inequalities for a superposition of the copson operator and the Hardy operator ⋮ Optimal embeddings of Bessel and Riesz type potentials on the basis of weighted Lorentz spaces ⋮ Generalized fractional maximal functions in Lorentz spaces Λ ⋮ Iterating Bilinear Hardy Inequalities ⋮ Some new iterated Hardy-type inequalities ⋮ Unnamed Item ⋮ Convolution in rearrangement-invariant spaces defined in terms of oscillation and the maximal function ⋮ A Class of Sub-elliptic Equations on the Heisenberg Group and Related Interpolation Inequalities ⋮ Some new iterated Hardy-type inequalities: the case \({\theta=1}\) ⋮ Reduction theorems for operators on the cones of monotone functions ⋮ Integral operators on cones of monotone functions ⋮ Some constructive criteria of optimal embeddings for potentials ⋮ Boundedness of weighted iterated Hardy-type operators involving suprema from weighted Lebesgue spaces into weighted Cesàro function spaces ⋮ Embeddings of Sobolev-type spaces into generalized Hölder spaces involving \(k\)-modulus of smoothness ⋮ Reduction theorems for weighted integral inequalities on the cone of monotone functions

Cites Work

• Embeddings of concave functions and duals of Lorentz spaces.
• Discretization and anti-discretization of rearrangement-invariant norms
• Weighted Lorentz spaces and the Hardy operator
• On the theory of spaces \(\Lambda\)
• Maximal Functions on Classical Lorentz Spaces and Hardy's Inequality with Weights for Nonincreasing Functions
• On the Principle of Duality in Lorentz Spaces
• The Weighted Hardy's Inequality for Nonincreasing Functions
• Integral Operators on the Cone of Monotone Functions
• Boundedness of Some Integral Operators
• Weak-type weights and normable Lorentz spaces
• The Weighted Hardy Inequality: New Proofs and the Case p = 1
• Embeddings and Duality Theorems for Weak Classical Lorentz Spaces

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