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Title: Weighted multidimensional inequalities for monotone functions (English)
Author: Barza, Sorina
Author: Persson, Lars-Erik
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 124
Issue: 2
Year: 1999
Pages: 329-335
Summary lang: English
Category: math
Summary: We discuss the characterization of the inequality \biggl(\int_{{\Bbb R}^N_+} f^q u\biggr)^{1/q} \leq C \biggl(\int_{{\Bbb R}^N_+} f^p v \biggr)^{1/p},\quad0<q, p <\infty, for monotone functions $f\geq0$ and nonnegative weights $u$ and $v$ and $N\geq1$. We prove a new multidimensional integral modular inequality for monotone functions. This inequality generalizes and unifies some recent results in one and several dimensions. (English)
Keyword: integral inequalities
Keyword: monotone functions
Keyword: several variables
Keyword: modular functions
Keyword: convex functions
Keyword: weakly convex functions
Keyword: weighted $L^p$ spaces
MSC: 26A48
MSC: 26B25
MSC: 26B99
MSC: 26D15
MSC: 46E30
idZBL: Zbl 0942.26028
idMR: MR1780701
DOI: 10.21136/MB.1999.126258
Date available: 2009-09-24T21:38:38Z
Last updated: 2020-07-29
Stable URL:
Reference: [1] Barza S., Persson L. E., Soria J.: Sharp weighted multidimensional integral inequalities for monotone functions.Math. Nachr. To appear. Zbl 0944.26025, MR 1738936
Reference: [2] Barza S., Persson L. E., Stepanov V. D.: On weighted multidimensional embeddings for monotone functions.Math. Scand. To appear. Zbl 1075.46507, MR 1839578
Reference: [3] Carro M. J., Pick L., Soria, J, Stepanov V. D.: On embeddings between classical Lorentz spaces.Research Report, 1998, submitted.
Reference: [4] Drábek P., Heinig H. P., Kufner A.: Weighted modular inequalities for monotone functions.J. Inequal. Appl. 1 (1997), 183-197. Zbl 0946.26014, MR 1731431
Reference: [5] Heinig H.P., Kufner A.: Hardy operators on monotone functions and sequences in Orlicz spaces.J. Lond. Math. Soc. 53 (2) (1996), 256-270. MR 1373059, 10.1112/jlms/53.2.256
Reference: [6] Heinig H., Lai Q.: Weighted modular inequalities for Hardy-type operators defined on monotone functions.Research Report, 1998, submitted.
Reference: [7] Krasnoseľski M. A., Ruticki, Ya.B.: Convex Functions and Orlìcz spaces.Noordhoff, Groningen, 1961. MR 0126722
Reference: [8] Stepanov V. D.: The weighted Hardy's inequality for nonincreasing functions.Trans. Amer. Math. Soc. 338 (1993), 173-186. Zbl 0786.26015, MR 1097171


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