Ulyanov-type Inequalities Between Lorentz–Zygmund Spaces

We establish inequalities of Ulyanov-type for moduli of smoothness relating the source Lorentz–Zygmund space L p , r ( log L ) α - γ , γ > 0 , and the target space L p ∗ , s ( log L ) α over R n if 1 < p < p ∗ < ∞ and over T n if 1 < p ≤ p ∗ < ∞ . The stronger logarithmic integrabi...

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Veröffentlicht in:	The Journal of fourier analysis and applications 2014-10, Vol.20 (5), p.1020-1049
Hauptverfasser:	Gogatishvili, Amiran, Opic, Bohumír, Tikhonov, Sergey, Trebels, Walter
Format:	Artikel
Sprache:	eng
Schlagworte:	Abstract Harmonic Analysis Algebra Analysis Approximations and Expansions Fourier Analysis Mathematical Methods in Physics Mathematics Mathematics and Statistics Numerical analysis Partial Differential Equations Signal,Image and Speech Processing
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Zusammenfassung:	We establish inequalities of Ulyanov-type for moduli of smoothness relating the source Lorentz–Zygmund space L p , r ( log L ) α - γ , γ > 0 , and the target space L p ∗ , s ( log L ) α over R n if 1 < p < p ∗ < ∞ and over T n if 1 < p ≤ p ∗ < ∞ . The stronger logarithmic integrability (corresponding to L p ∗ , s ( log L ) α ) is balanced by an additional logarithmic smoothness.
ISSN:	1069-5869 1531-5851
DOI:	10.1007/s00041-014-9343-4