Temat: maximal operators - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: On the maximal function for rotation invariant measures in $ℝ^{n}$
Autorzy:: Vargas, Ana M.
Powiązania:: https://bibliotekanauki.pl/articles/1290316.pdf
Data publikacji:: 1994
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: maximal operators
weak type estimates
Opis:: Given a positive measure μ in $ℝ^n$, there is a natural variant of the noncentered Hardy-Littlewood maximal operator $M_{μ}f(x) = sup_{x ∈ B} 1/μ(B) ʃ_{B} |f|dμ$, where the supremum is taken over all balls containing the point x. In this paper we restrict our attention to rotation invariant, strictly positive measures μ in $ℝ^n$. We give some necessary and sufficient conditions for $M_μ$ to be bounded from $L^{1}(dμ)$ to $L^{1,∞}(dμ)$.
Źródło:: Studia Mathematica; 1994, 110, 1; 9-17
0039-3223
Pojawia się w:: Studia Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Some weighted inequalities for general one-sided maximal operators
Autorzy:: J. Martín-Reyes, F.
de la Torre, A.
Powiązania:: https://bibliotekanauki.pl/articles/1220679.pdf
Data publikacji:: 1997
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: one-sided maximal operators
Cesàro averages
weights
Opis:: We characterize the pairs of weights on ℝ for which the operators $M_{h,k}^{+}f(x) = \underset{\text{sup}}{c>x}h(x,c) \int_{x}^{c} f(s)k(x,s,c)ds$ are of weak type (p,q), or of restricted weak type (p,q), 1 ≤ p < q < ∞, between the Lebesgue spaces with the coresponding weights. The functions h and k are positive, h is defined on ${(x,c): x < c}$, while k is defined on ${(x,s,c): x < s < c}$. If $h(x,c) = (c-x)^{-β}$, $k(x,s,c) = (c-s)^{α-1}$, 0 ≤ β ≤ α ≤ 1, we obtain the operator $M_{α,β}^{+}f = \underset{c>x}{\text{sup}} 1/(c-x)^{β} \int_{x}^{c} f(s)/(c-s)^{1-α} ds$. For this operator, under the assumption 1/p - 1/q = α - β, we extend the weak type characterization to the case p = q and prove that in the case of equal weights and 1 < p < ∞, weak and strong type are equivalent. If we take α = β we characterize the strong type weights for the operator $M_{α,α}^{+}$ introduced by W. Jurkat and J. Troutman in the study of $C_α$ differentiation of the integral.
Źródło:: Studia Mathematica; 1997, 122, 1; 1-14
0039-3223
Pojawia się w:: Studia Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: Weak type (1,1) multipliers on LCA groups
Autorzy:: Raposo, José A
Powiązania:: https://bibliotekanauki.pl/articles/1220262.pdf
Data publikacji:: 1997
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: weak type multipliers
maximal operators
vector inequalities
Opis:: In [ABB] Asmar, Berkson and Bourgain prove that for a sequence ${ϕ_j}^∞_{j=1} $ of weak type (1, 1) multipliers in $ℝ^n$ and a function $k ∈ L^1(ℝ^n)$ the weak type (1,1) constant of the maximal operator associated with ${k⁎ϕ_j}_j$ is controlled by that of the maximal operator associated with ${ϕ_j}_j$. In [ABG] this theorem is extended to LCA groups with an extra hypothesis: the multipliers must be continuous. In this paper we prove a more general version of this last result without assuming the continuity of the multipliers. The proof arises after simplifying the one in [ABB] which becomes then extensible to LCA groups.
Źródło:: Studia Mathematica; 1997, 122, 2; 123-130
0039-3223
Pojawia się w:: Studia Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 4.

Tytuł:: Discrete Hardy spaces
Autorzy:: Boza, Santiago
Carro, María
Powiązania:: https://bibliotekanauki.pl/articles/1218496.pdf
Data publikacji:: 1998
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: Hardy spaces
discrete Hilbert transform
maximal operators
Opis:: We study various characterizations of the Hardy spaces $H^p(ℤ)$ via the discrete Hilbert transform and via maximal and square functions. Finally, we present the equivalence with the classical atomic characterization of $H^p(ℤ)$ given by Coifman and Weiss in [CW]. Our proofs are based on some results concerning functions of exponential type.
Źródło:: Studia Mathematica; 1998, 129, 1; 31-50
0039-3223
Pojawia się w:: Studia Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 5.

Tytuł:: Maximal functions and smoothness spaces in $L_{p}(ℝ^{d})
Autorzy:: Kyriazis, G. C.
Powiązania:: https://bibliotekanauki.pl/articles/1218547.pdf
Data publikacji:: 1998
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: maximal functions
approximation by operators
wavelets
smoothness spaces
Opis:: 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.
Źródło:: Studia Mathematica; 1998, 128, 3; 219-241
0039-3223
Pojawia się w:: Studia Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

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