Notes on inequalities with doubling weights

Journal of Approximation Theory

Volumn 100, Issue 1, 1999, Pages 60-72

  Erdélyi, Tamás ^a  

^a TEXAS A AND M UNIVERSITY   (United States)

Author keywords

A weights; Bernstein's inequality; Christoffel function; Doubling weights; Marcinkiewicz inequality; Nikolskii inequality; Remez inequality

Indexed keywords

EID: 0033196037     PISSN: 00219045     EISSN: None     Source Type: Journal    
DOI: 10.1006/jath.1999.3340     Document Type: Article

References (13)

1. V. V. Arestov, On inequalities for trigonometric polynomials and their derivatives, Izv. Akad. Nauk SSSR Ser. Mat. 45 (1981), 3-22.
2. V. M. Badkov, Asymptotic and extremal properties of orthogonal polynomials in the presence of singularities in the weight, Proc. Steklov Inst. Math. (1994), 37-82.
3. T. Erdélyi, Bernstein and Markov type inequalities for generalized nonnegative polynomials, Canad. J. Math. 43, No. 3 (1991), 495-505.
4. T. Erdélyi, Remez-type inequalities and their applications, J. Comput. Appl. Math. 47 (1993), 167-209.
5. T. Erdélyi, Nikolskii-type inequalities for generalized polynomials and zeros of orthogonal polynomials, J. Approx. Theory 67 (1991), 80-92.
6. T. Erdélyi, Remez-type inequalities on the size of generalized polynomials, J. London Math. Soc. 45 (1992), 255-264.
7. C. Fefferman and B. Muckenhoupt, Two nonequivalent conditions for weight functions, Proc. Amer. Math. Soc. 45 (1994), 99-104.
8. K. G. Ivanov and V. Totik, Fast decreasing polynomials, Constr. Approx. 6 (1990), 1-20.
9. μ-spaces, Studia Sci. Math. Hungar. 28 (1993), 183-188.
10. D. Lubinsky, A. Máté, and P. Nevai, Quadrature sums involving pth powers of polynomials, SIAM J. Math. Anal. 18 (1987), 531-544.
11. G. Mastroianni, Some weighted polynomial inequalities, J. Comput. Appl. Math. 65 (1995), 279-292.
12. ∞ weights, Constr. Approx., in Press.
13. E. M. Stein, "Harmonic Analysis," Princeton Univ. Press, Princeton, NJ, 1993.