An equivalence theorem for some integral conditions with general measures related to Hardy´s inequality

• It is proved that, besides the usual Muckenhoupt condition, there exist four different scales of conditions for characterizing the Hardy type inequality with general measures for the case 1<pq<∞. In fact, an even more general equivalence theorem of independent interest is proved and discussed.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

Keyword

Inequalities

Hardy's inequality

Discrete Hardy's inequality

Hardy operator

Hardy's inequality with general measures

Scales of characterizations

Weight functions

Weight sequences

Equivalent integral conditions

Comparisons

MATHEMATICS

MATEMATIK

Matematik

Publication and Content Type

ref (subject category)

art (subject category)