Mapping properties of integral averaging operators

H. Heinig; G. Sinnamon

Displaying similar documents to “Mapping properties of integral averaging operators”

Weighted inequalities for monotone and concave functions

Hans Heinig, Lech Maligranda (1995)

Studia Mathematica

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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.

Weighted Hardy inequalities and Hardy transforms of weights

Joan Cerdà, Joaquim Martín (2000)

Studia Mathematica

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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 inequalities for the two-dimensional Hardy operator

E. Sawyer (1985)

Studia Mathematica

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First and second order Opial inequalities

Steven Bloom (1997)

Studia Mathematica

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Let $T_{γ} f (x) = ʃ_{0}^{x} k {(x, y)}^{γ} f (y) d y$ , where k is a nonnegative kernel increasing in x, decreasing in y, and satisfying a triangle inequality. An nth-order Opial inequality has the form $ʃ_{0}^{\infty} (\prod_{i = 1}^{n} | T_{γ_{i}} {f (x) |}^{q_{i}} {|) | f (x) |}^{q_{0}} w (x) d x \leq C (ʃ_{0}^{\infty} {| f (x) |}^{p} {v (x) d x)}^{(q_{0} + \dots + q_{n}) / p}$ . Such inequalities can always be simplified to nth-order reduced inequalities, where the exponent $q_{0} = 0$ . When n = 1, the reduced inequality is a standard weighted norm inequality, and characterizing the weights is easy. We also find necessary and sufficient conditions on the weights for second-order reduced Opial inequalities to hold. ...

Weighted Lorentz norm inequalities for integral operators

Elida Ferreyra (1990)

Studia Mathematica

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Weighted norm inequalities for Riesz potentials and fractional maximal functions in mixed norm Lebesgue spaces

Tord Sjödin (1990)

Studia Mathematica

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Embeddings of concave functions and duals of Lorentz spaces.

Gord Sinnamon (2002)

Publicacions Matemàtiques

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A simple expression is presented that is equivalent to the norm of the L^p _v → L^q _u embedding of the cone of quasi-concave functions in the case 0 < q < p < ∞. The result is extended to more general cones and the case q = 1 is used to prove a reduction principle which shows that questions of boundedness of operators on these cones may be reduced to the boundedness...

$L^{p}$ weighted inequalities for the dyadic square function

Akihito Uchiyama (1995)

Studia Mathematica

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We prove that $ʃ {(S_{d} f)}^{p} V d x \leq C_{p, n} ʃ {| f |}^{p} M_{d}^{([p / 2] + 2)} V d x$ , where $S_{d}$ is the dyadic square function, $M_{d}^{(k)}$ is the k-fold application of the dyadic Hardy-Littlewood maximal function and p > 2.

Sharp $L^{p}$ -weighted Sobolev inequalities

Carlos Pérez (1995)

Annales de l'institut Fourier

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We prove sharp weighted inequalities of the form $\int_{R^{n}} | f (x) |^{p} v (x) d x \leq C \int_{R^{n}} | q (D) (f) (x) |^{p} N (v) (x) d x$ where $q (D)$ is a differential operator and $N$ is a combination of maximal type operator related to $q (D)$ and to $p$ .

Weighted norm inequalities and Schur's Lemma

Michael Christ (1984)

Studia Mathematica

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