Geodesic
On maximal overdetermined Hardy's inequality of second order on a finite interval
Mathematica Bohemica, Tome 124 (1999) no. 2-3, pp. 293-302

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
A characterization of the weighted Hardy inequality \left\| Fu \right\| _2 \le C \left\| F"v \right\| _2,\^^MF(0)=F'(0)=F(1)=F'(1)=0 is given.
A characterization of the weighted Hardy inequality \left\| Fu \right\| _2 \le C \left\| F"v \right\| _2,\^^MF(0)=F'(0)=F(1)=F'(1)=0 is given.
DOI : 10.21136/MB.1999.126245
Classification : 26D10, 34B05, 46N20
Keywords: weighted Hardy’s inequality 
Nasyrova, Maria; Stepanov, Vladimir. On maximal overdetermined Hardy's inequality of second order on a finite interval. Mathematica Bohemica, Tome 124 (1999) no. 2-3, pp. 293-302. doi: 10.21136/MB.1999.126245
@article{10_21136_MB_1999_126245,
     author = {Nasyrova, Maria and Stepanov, Vladimir},
     title = {On maximal overdetermined {Hardy's} inequality of second order on a finite interval},
     journal = {Mathematica Bohemica},
     pages = {293--302},
     year = {1999},
     volume = {124},
     number = {2-3},
     doi = {10.21136/MB.1999.126245},
     mrnumber = {1780698},
     zbl = {0936.26010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.1999.126245/}
}
TY  - JOUR
AU  - Nasyrova, Maria
AU  - Stepanov, Vladimir
TI  - On maximal overdetermined Hardy's inequality of second order on a finite interval
JO  - Mathematica Bohemica
PY  - 1999
SP  - 293
EP  - 302
VL  - 124
IS  - 2-3
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.1999.126245/
DO  - 10.21136/MB.1999.126245
LA  - en
ID  - 10_21136_MB_1999_126245
ER  - 
%0 Journal Article
%A Nasyrova, Maria
%A Stepanov, Vladimir
%T On maximal overdetermined Hardy's inequality of second order on a finite interval
%J Mathematica Bohemica
%D 1999
%P 293-302
%V 124
%N 2-3
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.1999.126245/
%R 10.21136/MB.1999.126245
%G en
%F 10_21136_MB_1999_126245

[1] Drábek P., Kufner A.: The Hardy inequalities and Birkhoff interpolation. Bayreuther Math. Schriften 47 (1994), 99-104. | MR

[2] Gurka P.: Generalized Hardy inequalities for functions vanishing on both ends of the interval. Preprint, 1987.

[3] Edmunds D. E., Evans W. D., Harris D. J.: Approximation numbers of certain Volterra integral operators. J. London Math. Soc., II. Ser. 37 (1988), 471-489. | DOI | MR | Zbl

[4] Edmunds D. E., Stepanov V. D.: The measure of non-compactness and approximation numbers of certain Volterra integral operators. Math. Ann. 298 (1994), 41-66. | DOI | MR | Zbl

[5] Heinig H. P., Kufner A.: Hardy's inequality for higher order derivatives. Proc. Steklov Inst. Math. 192 (1992), 113-121. | MR

[6] Kufner A.: Higher order Hardy inequalities. Bayreuther Math. Schriften 44 (1993), 105-146. | MR | Zbl

[7] Kufner A., Leinfelder H.: On overdetermined Hardy inequalities. Preprint, 1998. | MR | Zbl

[8] Kufner A., Simader C. G.: Hardy inequalities for overdetermined classes of functions. Z. Anal. Anwend. 16 (1997), no. 2, 387-403. | DOI | MR | Zbl

[9] Kufner A., Sinnamon G.: Overdetermined Hardy inequalities. J. Math. Anal. Appl. 213 (1997), 468-486. | DOI | MR | Zbl

[10] Kufner A., Wannebo A.: Some remarks on the Hardy inequality for higher order derivatives. General Inequalities VI. Internat. Series of Numer. Math. Vol. 103, Birkhäuser Verlag, Basel, 1992, pp. 33-48. | MR | Zbl

[11] Nasyrova M., Stepanov V.: On weighted Hardy inequalities on semiaxis for functions vanishing at the endpoints. J. InequaL Appl. 1 (1997), 223-238. | MR | Zbl

[12] Nasyrova M.: Overdetermined weighted Hardy inequalities on semiaxis. Proceedings of Dehli conference. To appear. | MR | Zbl

[13] Opic B., Kufner A.: Hardy-type Inequalities. Pitman Research Notes in Math., Series 219, Longman Sci&Tech., Harlow, 1990. | MR | Zbl

[14] Rudin W.: Functional Analysis. McGraw-Hill Book Company, New York, 1973. | MR | Zbl

[15] Sinnamon G.: Kufner's conjecture for higher order Hardy inequalities. Real Analysis Exchange, 21 (1995/96), 590-603. | DOI | MR | Zbl

[16] Stepanov V. D.: Weighted inequalities for a class of Volterra convolution operators. J. London Math. Soc. (2) 45 (1992), 232-242. | DOI | MR | Zbl

[17] Stepanov V. D.: Weighted norm inequalities of Hardy type for a class of integral operators. J. London Math. Soc. (2) 50 (1994), 105-120. | DOI | MR | Zbl

Cité par Sources :