| 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:
|
http://hdl.handle.net/10338.dmlcz/126258 |
| . |
| 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 |
| . |
