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The Jawerth–Franke Embedding of Spaces with Dominating Mixed Smoothness
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Markus Hansen
Published/Copyright:
March 11, 2010
Abstract
We give a proof of the Jawerth embedding for function spaces with dominating mixed smoothness of Besov and Triebel–Lizorkin type
where
0 < 𝑝0 < 𝑝1 ≤ ∞ and 0 < 𝑞0,𝑞1 ≤ ∞
and
with
If 𝑝1 < ∞, we prove also the Franke embedding
Our main tools are discretization by a wavelet isomorphism and multivariate rearrangements.
Key words and phrases:: Besov spaces; Triebel–Lizorkin spaces; Sobolev embedding; dominating mixed smoothness; Jawerth–Franke embedding
Received: 2008-10-03
Revised: 2008-10-27
Published Online: 2010-03-11
Published in Print: 2009-December
© Heldermann Verlag
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Keywords for this article
Besov spaces;
Triebel–Lizorkin spaces;
Sobolev embedding;
dominating mixed smoothness;
Jawerth–Franke embedding
Articles in the same Issue
- On the Necessary and Sufficient Conditions for the Stability of Linear Generalized Ordinary Differential, Linear Impulsive and Linear Difference Systems
- Nonlinear Three-Point Boundary Value Problems for a Class of Impulsive Functional Differential Equations
- Unilateral Contact Problems with Friction for Hemitropic Elastic Solids
- A Periodic Boundary Value Problem for Functional Differential Equations of Higher Order
- The Jawerth–Franke Embedding of Spaces with Dominating Mixed Smoothness
- Stability by Fixed Point Theory for Nonlinear Delay Difference Equations
- On the Rates of Convergence of Chlodovsky–Durrmeyer Operators and their Bézier Variant
- On Nonmeasurable Functions of Two Variables and Iterated Integrals
- Bounded and Vanishing at Infinity Solutions of Nonlinear Differential Systems
- On Functional Equations Connected with Quadrature Rules
- The Riemann–Hilbert Problem in a Domain with Piecewise Smooth Boundaries in Weight Classes of Cauchy Type Integrals with a Density from Variable Exponent Lebesgue Spaces
- A Counterexample on Embedding of Spaces
- On Solutions of a Singular Viscoelastic Equation with an Integral Condition
- Nonbounding 𝑛-C.E. 𝑄-Degrees
- Nonequivalence of Unilateral Strong Differentiation Bases in
