SUFFICIENT CONDITIONS FOR THREE WEIGHT SUM INEQUALITIES IN LEBESGUE SPACES

SUFFICIENT CONDITIONS FOR THREE WEIGHT SUM INEQUALITIES IN LEBESGUE SPACES

Conditions (in terms of integrals of the weights) are derived, under which the weighted Lq-norm of the j-th order derivative of the function u can be estimated by the sum of the weighted Lr-norm of u and of the weighted Lp-norm of its m-th order derivative, j < m. All mutual positions of the para...

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Veröffentlicht in:Real analysis exchange 1996, Vol.22 (1), p.292-317
Hauptverfasser: Brown, Richard C., Hinton, Don B., Kufner, Alois
Format: Artikel
Sprache:eng
Schlagworte:
26D10
46E30
Embeddings
Grants
Interpolation
interpolation inequalities
Lebesgue spaces
Mathematical functions
Mathematical independent variables
Mathematical inequalities
Sobolev spaces
Sufficient conditions
weighted inequalities
weighted Sobolev space
Weighting functions
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Zusammenfassung:Conditions (in terms of integrals of the weights) are derived, under which the weighted Lq-norm of the j-th order derivative of the function u can be estimated by the sum of the weighted Lr-norm of u and of the weighted Lp-norm of its m-th order derivative, j < m. All mutual positions of the parameters, p, q, r are admissible.
ISSN:0147-1937
1930-1219
DOI:10.2307/44152752