Displaying similar documents to “First and second order Opial inequalities”

Weighted Hardy inequalities and Hardy transforms of weights

Joan Cerdà, Joaquim Martín (2000)

Studia Mathematica

Similarity:

Many problems in analysis are described as weighted norm inequalities that have given rise to different classes of weights, such as A p -weights of Muckenhoupt and B p -weights of Ariño and Muckenhoupt. Our purpose is to show that different classes of weights are related by means of composition with classical transforms. A typical example is the family M p of weights w for which the Hardy transform is L p ( w ) -bounded. A B p -weight is precisely one for which its Hardy transform is in M p , and also a weight...

Weighted L Φ integral inequalities for operators of Hardy type

Steven Bloom, Ron Kerman (1994)

Studia Mathematica

Similarity:

Necessary and sufficient conditions are given on the weights t, u, v, and w, in order for Φ 2 - 1 ( ʃ Φ 2 ( w ( x ) | T f ( x ) | ) t ( x ) d x ) ≤ Φ 1 - 1 ( ʃ Φ 1 ( C u ( x ) | f ( x ) | ) v ( x ) d x ) to hold when Φ 1 and Φ 2 are N-functions with Φ 2 ∘ Φ 1 - 1 convex, and T is the Hardy operator or a generalized Hardy operator. Weak-type characterizations are given for monotone operators and the connection between weak-type and strong-type inequalities is explored.

A remark on Fefferman-Stein's inequalities.

Y. Rakotondratsimba (1998)

Collectanea Mathematica

Similarity:

It is proved that, for some reverse doubling weight functions, the related operator which appears in the Fefferman Stein's inequality can be taken smaller than those operators for which such an inequality is known to be true.

Weighted inequalities for monotone and concave functions

Hans Heinig, Lech Maligranda (1995)

Studia Mathematica

Similarity:

Characterizations of weight functions are given for which integral inequalities of monotone and concave functions are satisfied. The constants in these inequalities are sharp and in the case of concave functions, constitute weighted forms of Favard-Berwald inequalities on finite and infinite intervals. Related inequalities, some of Hardy type, are also given.

Two weighted inequalities for convolution maximal operators.

Ana Lucía Bernardis, Francisco Javier Martín-Reyes (2002)

Publicacions Matemàtiques

Similarity:

Let φ: R → [0,∞) an integrable function such that φχ = 0 and φ is decreasing in (0,∞). Let τf(x) = f(x-h), with h ∈ R {0} and f(x) = 1/R f(x/R), with R > 0. In this paper we characterize the pair of weights (u, v) such that the operators Mf(x) = sup|f| * [τφ](x) are of weak type (p, p) with respect to (u, v), 1 < p < ∞.