Some scales of equivalent weight characterizations of Hardy´s inequality: the case q < p

• We consider the weighted Hardy inequality                                                1/q                            1/p                                       q                      ∞                                       ∞                             x                                                                 f p (x)v(x)dx                               f (t)dt   u(x)dx       C                    0      0                                0for the case 0 < q < p < ∞, p > 1 . The weights u(x) and v(x) for which this inequalityholds for all f (x)    0 may be characterized by the Mazya-Rosin or by the Persson-Stepanovconditions. In this paper, we show that these conditions are not unique and can be supplementedby some continuous scales of conditions and we prove their equivalence. The results for the dualoperator which do not follow by duality when 0 < q < 1 are also given.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

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

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

Nyckelord

integral inequalities

weighted Hardy’s inequality

MATHEMATICS

MATEMATIK

Matematik

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