### Weighted Orlicz-Type Integral Inequalities for the Hardy
                Operator

C. J. Neugebauer
Source: Real Anal. Exchange Volume 32, Number 2 (2006), 495-510.

#### Abstract

We study integral inequalities for the Hardy operator $Hf$ of the form $\int_0^\infty\Phi[Hf^p]\,d\mu\leq c_0\int_0^\infty\Phi[c_1f^p]\,d\mu$, where $\Phi$ is convex, $\mu$ is a measure on $\mathbb R_+$, $1\leq p < \infty$, and $f$ is non-increasing. The results we obtain are extensions of the classical $B_p-$ weight theory [1,5].

First Page:
Primary Subjects: 42B25, 42B35
Keywords: weights; Hardy operato
Full-text: Open access
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 8, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.7854352593421936, "perplexity_flag": "middle"}