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1
Content available remote

On weak minima of certain integral functionals

100%
Moscariello G.
Annales Polonici Mathematici
|
1998
|
tom 69
|
nr 1
37-48
EN
We prove a regularity result for weak minima of integral functionals of the form $∫_Ω F(x,Du) dx$ where F(x,ξ) is a Carathéodory function which grows as $|ξ|^p$ with some p > 1.
2
Content available remote

Maximal functions and smoothness spaces in $L_{p}(ℝ^{d})

80%
Kyriazis G. C.
Studia Mathematica
|
1998
|
tom 128
|
nr 3
219-241
EN
We study smoothness spaces generated by maximal functions related to the local approximation errors of integral operators. It turns out that in certain cases these smoothness classes coincide with the spaces $C^α_p(ℝ^d)$, 0 < p≤∞, introduced by DeVore and Sharpley [DS] by means of the so-called sharp maximal functions of Calderón and Scott. As an application we characterize the $C^α_p(ℝ^d)$ spaces in terms of the coefficients of wavelet decompositions.
3
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On the maximal operator associated with the free Schrödinger equation

80%
Wang S.
Studia Mathematica
|
1997
|
tom 122
|
nr 2
167-182
EN
For d > 1, let $(S_{d}f)(x,t) = ʃ_{ℝ^n} e^{ix·ξ} e^{it|ξ|^d} f̂(ξ)dξ$, $x ∈ ℝ^n$, where f̂ is the Fourier transform of $f ∈ S (ℝ^n)$, and $(S_{d}*f)(x) = sup_{0 < t < 1} |(S_{d}f)(x,t)|$ its maximal operator. P. Sjölin ([11]) has shown that for radial f, the estimate (*) $(ʃ_{|x| < R} |(S_{d}*f)(x)|^p dx)^{1/p} ≤ C_{R}∥f∥_{H_{1/4}}$ holds for p = 4n/(2n-1) and fails for p > 4n/(2n-1). In this paper we show that for non-radial f, (*) fails for p > 2. A similar result is proved for a more general maximal operator.
4
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An exponential estimate for convolution powers

80%
Jones R. L.
Studia Mathematica
|
1999
|
tom 137
|
nr 2
195-202
EN
We establish an exponential estimate for the relationship between the ergodic maximal function and the maximal operator associated with convolution powers of a probability measure.
5
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Local Hardy spaces on Chébli-Trimèche hypergroups

80%
Bloom W. R., Xu Z.
Studia Mathematica
|
1999
|
tom 133
|
nr 3
197-230
EN
We investigate the local Hardy spaces $h^p$ on Chébli-Trimèche hypergroups, and establish the equivalence of various characterizations of these in terms of maximal functions and atomic decomposition.
6
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Weighted estimates for commutators of linear operators

80%
Alvarez J., Bagby R. J., Kurtz D. S., Pérez C.
Studia Mathematica
|
1993
|
tom 104
|
nr 2
195-209
EN
We study boundedness properties of commutators of general linear operators with real-valued BMO functions on weighted $L^p$ spaces. We then derive applications to particular important operators, such as Calderón-Zygmund type operators, pseudo-differential operators, multipliers, rough singular integrals and maximal type operators.
7
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Intrinsic characterizations of distribution spaces on domains

61%
Rychkov V. S.
Studia Mathematica
|
1998
|
tom 127
|
nr 3
277-298
EN
We give characterizations of Besov and Triebel-Lizorkin spaces $B_{pq}^{s}(Ω)$ and $F_{pq}^s(Ω)$ in smooth domains $Ω ⊂ ℝ^n$ via convolutions with compactly supported smooth kernels satisfying some moment conditions. The results for s ∈ ℝ, 0 < p,q ≤ ∞ are stated in terms of the mixed norm of a certain maximal function of a distribution. For s ∈ ℝ, 1 ≤ p ≤ ∞, 0 < q ≤ ∞ characterizations without use of maximal functions are also obtained.
8
Content available remote

Distribution and rearrangement estimates of the maximal function and interpolation

51%
U. Asekritova I., Krugljak N. Y., Maligranda L., Persson L.-E.
Studia Mathematica
|
1997
|
tom 124
|
nr 2
107-132
EN
There are given necessary and sufficient conditions on a measure dμ(x)=w(x)dx under which the key estimates for the distribution and rearrangement of the maximal function due to Riesz, Wiener, Herz and Stein are valid. As a consequence, we obtain the equivalence of the Riesz and Wiener inequalities which seems to be new even for the Lebesgue measure. Our main tools are estimates of the distribution of the averaging function f** and a modified version of the Calderón-Zygmund decomposition. Analogous methods allow us to obtain K-functional formulas in terms of the maximal function for couples of weighted $L_p$-spaces.
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