Real Analysis Exchange
- Real Anal. Exchange
- Volume 22, Number 1 (1996), 292-317.
Sufficient conditions for three weight sum inequalities in Lebesgue spaces
Conditions (in terms of integrals of the weights) are derived, under which the weighted \(L^q\)-norm of the \(j\)-th order derivative of the function \(u\) can be estimated by the sum of the weighted \(L^r\)-norm of \(u\) and of the weighted \(L^p\)-norm of its \(m\)-th order derivative, \(j\lt m\). All mutual positions of the parameters, \(p,\, q, \, r\) are admissible.
Real Anal. Exchange, Volume 22, Number 1 (1996), 292-317.
First available in Project Euclid: 1 June 2012
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 26D10: Inequalities involving derivatives and differential and integral operators 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Brown, Richard C.; Hinton, Don B.; Kufner, Alois. Sufficient conditions for three weight sum inequalities in Lebesgue spaces. Real Anal. Exchange 22 (1996), no. 1, 292--317. https://projecteuclid.org/euclid.rae/1338515222