# Weighted multidimensional inequalities for monotone functions

Sorina Barza; Lars-Erik Persson

Mathematica Bohemica (1999)

- Volume: 124, Issue: 2-3, page 329-335
- ISSN: 0862-7959

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topBarza, Sorina, and Persson, Lars-Erik. "Weighted multidimensional inequalities for monotone functions." Mathematica Bohemica 124.2-3 (1999): 329-335. <http://eudml.org/doc/248465>.

@article{Barza1999,

abstract = {We discuss the characterization of the inequality
(RN+ fq u)1/q C (RN+ fp v )1/p, 0<q, p <,
for monotone functions $f\ge 0$ and nonnegative weights $u$ and $v$ and $N\ge 1$. We prove a new multidimensional integral modular inequality for monotone functions. This inequality generalizes and unifies some recent results in one and several dimensions.},

author = {Barza, Sorina, Persson, Lars-Erik},

journal = {Mathematica Bohemica},

keywords = {integral inequalities; monotone functions; several variables; modular functions; convex functions; weakly convex functions; weighted $L^p$ spaces; integral inequalities; monotone functions; several variables; weighted spaces; modular functions; convex functions; weakly convex functions},

language = {eng},

number = {2-3},

pages = {329-335},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Weighted multidimensional inequalities for monotone functions},

url = {http://eudml.org/doc/248465},

volume = {124},

year = {1999},

}

TY - JOUR

AU - Barza, Sorina

AU - Persson, Lars-Erik

TI - Weighted multidimensional inequalities for monotone functions

JO - Mathematica Bohemica

PY - 1999

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 124

IS - 2-3

SP - 329

EP - 335

AB - We discuss the characterization of the inequality
(RN+ fq u)1/q C (RN+ fp v )1/p, 0<q, p <,
for monotone functions $f\ge 0$ and nonnegative weights $u$ and $v$ and $N\ge 1$. We prove a new multidimensional integral modular inequality for monotone functions. This inequality generalizes and unifies some recent results in one and several dimensions.

LA - eng

KW - integral inequalities; monotone functions; several variables; modular functions; convex functions; weakly convex functions; weighted $L^p$ spaces; integral inequalities; monotone functions; several variables; weighted spaces; modular functions; convex functions; weakly convex functions

UR - http://eudml.org/doc/248465

ER -

## References

top- Barza S., Persson L. E., Soria J., Sharp weighted multidimensional integral inequalities for monotone functions, Math. Nachr. To appear. Zbl0944.26025MR1738936
- Barza S., Persson L. E., Stepanov V. D., On weighted multidimensional embeddings for monotone functions, Math. Scand. To appear. Zbl1075.46507MR1839578
- Carro M. J., Pick L., Soria, J, Stepanov V. D., On embeddings between classical Lorentz spaces, Research Report, 1998, submitted. (1998)
- Drábek P., Heinig H. P., Kufner A., Weighted modular inequalities for monotone functions, J. Inequal. Appl. 1 (1997), 183-197. (1997) Zbl0946.26014MR1731431
- Heinig H.P., Kufner A., 10.1112/jlms/53.2.256, J. Lond. Math. Soc. 53 (2) (1996), 256-270. (1996) MR1373059DOI10.1112/jlms/53.2.256
- Heinig H., Lai Q., Weighted modular inequalities for Hardy-type operators defined on monotone functions, Research Report, 1998, submitted. (1998)
- Krasnoseľski M. A., Ruticki, Ya.B., Convex Functions and Orlìcz spaces, Noordhoff, Groningen, 1961. (1961) MR0126722
- Stepanov V. D., The weighted Hardy's inequality for nonincreasing functions, Trans. Amer. Math. Soc. 338 (1993), 173-186. (1993) Zbl0786.26015MR1097171

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