Behaviour of -Dini singular integrals in weighted spaces
Osvaldo Capri, Carlos Segovia (1989)
Studia Mathematica
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Osvaldo Capri, Carlos Segovia (1989)
Studia Mathematica
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Xiaosha Zhou, Lanzhe Liu (2013)
Colloquium Mathematicae
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Some weighted sharp maximal function inequalities for the Toeplitz type operator are established, where are a fixed singular integral operator with non-smooth kernel or ±I (the identity operator), are linear operators defined on the space of locally integrable functions, k = 1,..., m, and . The weighted boundedness of on Morrey spaces is obtained by using sharp maximal function inequalities.
Carnot D. Kenfack, Benoît F. Sehba (2016)
Colloquium Mathematicae
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Let ω be a Békollé-Bonami weight. We give a complete characterization of the positive measures μ such that and , where is the weighted Hardy-Littlewood maximal function on the upper half-plane and 1 ≤ p,q <; ∞.
Gladis Pradolini, Jorgelina Recchi (2018)
Czechoslovak Mathematical Journal
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Let be a nonnegative Borel measure on satisfying that for every cube , where is the side length of the cube and . We study the class of pairs of weights related to the boundedness of radial maximal operators of fractional type associated to a Young function in the context of non-homogeneous spaces related to the measure . Our results include two-weighted norm and weak type inequalities and pointwise estimates. Particularly, we give an improvement of a two-weighted result...
C. J. Neugebauer (2009)
Studia Mathematica
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Let be the Ariõ-Muckenhoupt weight class which controls the weighted -norm inequalities for the Hardy operator on non-increasing functions. We replace the constant p by a function p(x) and examine the associated -norm inequalities of the Hardy operator.
Qingying Xue (2013)
Studia Mathematica
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The following iterated commutators of the maximal operator for multilinear singular integral operators and of the multilinear fractional integral operator are introduced and studied: , , where are the smooth truncations of the multilinear singular integral operators and is the multilinear fractional integral operator, for i = 1,…,m and f⃗ = (f1,…,fm). Weighted strong and L(logL) type end-point estimates for the above iterated commutators associated with two classes of multiple...
L. de Rosa, C. Segovia (2006)
Studia Mathematica
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We study the boundedness of the one-sided operator between the weighted spaces and for every weight w. If λ = 2/p whenever 1 < p < 2, and in the case p = 1 for λ > 2, we prove the weak type of . For every λ > 1 and p = 2, or λ > 2/p and 1 < p < 2, the boundedness of this operator is obtained. For p > 2 and λ > 1, we obtain the boundedness of from to , where denotes the operator M¯ iterated k times.
Paul Alton Hagelstein (2001)
Studia Mathematica
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Let denote the strong maximal operator. Let and denote the one-dimensional Hardy-Littlewood maximal operators in the horizontal and vertical directions in ℝ². A function h supported on the unit square Q = [0,1]×[0,1] is exhibited such that but . It is shown that if f is a function supported on Q such that but , then there exists a set A of finite measure in ℝ² such that .
Dorothee D. Haroske (2011)
Banach Center Publications
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We study continuity envelopes of function spaces and where the weight belongs to the Muckenhoupt class ₁. This essentially extends partial forerunners in [13, 14]. We also indicate some applications of these results.
José García-Cuerva
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CONTENTSIntroduction.......................................................................................................................................................... 5Chapter I. Some preliminary lemmas............................................................................................................ 8Chapter II. Weighted spaces of analytic functions.......................................................................... 13 1. Behaviour at the boundary..........................................................................................................................
Keiji Izuchi (2004)
Studia Mathematica
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Let μ and λ be bounded positive singular measures on the unit circle such that μ ⊥ λ. It is proved that there exist positive measures μ₀ and λ₀ such that μ₀ ∼ μ, λ₀ ∼ λ, and , where is the associated singular inner function of μ. Let be the common zeros of equivalent singular inner functions of . Then (μ) ≠ ∅ and (μ) ∩ (λ) = ∅. It follows that μ ≪ λ if and only if (μ) ⊂ (λ). Hence (μ) is the set in the maximal ideal space of which relates naturally to the set of measures equivalent...
Amiran Gogatishvili, Rza Mustafayev, Tuğçe Ünver (2017)
Czechoslovak Mathematical Journal
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In this paper, characterizations of the embeddings between weighted Copson function spaces and weighted Cesàro function spaces are given. In particular, two-sided estimates of the optimal constant in the inequality where , and , , , are weights on , are obtained. The most innovative part consists of the fact that possibly different parameters and and possibly different inner weights and are allowed. The proof is based on the combination of duality techniques...
Wei Ding, Jiao Chen, Yaoming Niu (2019)
Czechoslovak Mathematical Journal
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We study the duality theory of the weighted multi-parameter Triebel-Lizorkin spaces . This space has been introduced and the result for has been proved in Ding, Zhu (2017). In this paper, for , we establish its dual space .
Suying Liu, Minghua Yang (2018)
Czechoslovak Mathematical Journal
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Let be a non-negative self-adjoint operator acting on satisfying a pointwise Gaussian estimate for its heat kernel. Let be an weight on , . In this article we obtain a weighted atomic decomposition for the weighted Hardy space , associated to . Based on the atomic decomposition, we show the dual relationship between and .
Kristóf Szarvas, Ferenc Weisz (2016)
Czechoslovak Mathematical Journal
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The classical Hardy-Littlewood maximal operator is bounded not only on the classical Lebesgue spaces (in the case ), but (in the case when is log-Hölder continuous and ) on the variable Lebesgue spaces , too. Furthermore, the classical Hardy-Littlewood maximal operator is of weak-type . In the present note we generalize Besicovitch’s covering theorem for the so-called -rectangles. We introduce a general maximal operator and with the help of generalized -functions, the strong-...
V.A. Rukavishnikov, E.V. Matveeva, E.I. Rukavishnikova (2018)
Communications in Mathematics
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We study the properties of the weighted space and weighted set for boundary value problem with singularity.
R. Demazeux (2011)
Studia Mathematica
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We complete the different cases remaining in the estimation of the essential norm of a weighted composition operator acting between the Hardy spaces and for 1 ≤ p,q ≤ ∞. In particular we give some estimates for the cases 1 = p ≤ q ≤ ∞ and 1 ≤ q < p ≤ ∞.
Adam Osękowski (2014)
Banach Center Publications
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We prove sharp a priori estimates for the distribution function of the dyadic maximal function ℳ ϕ, when ϕ belongs to the Lorentz space , 1 < p < ∞, 1 ≤ q < ∞. The approach rests on a precise evaluation of the Bellman function corresponding to the problem. As an application, we establish refined weak-type estimates for the dyadic maximal operator: for p,q as above and r ∈ [1,p], we determine the best constant such that for any , .
Ahmad K. Al Abdulaali, Hassine El Mir (2020)
Czechoslovak Mathematical Journal
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We discuss the existence of the current , for positive and closed currents and unbounded plurisubharmonic functions . Furthermore, a new type of weighted Lelong number is introduced under the name of weight Lelong number.
Xin-Cui Guo, Ze-Hua Zhou (2015)
Czechoslovak Mathematical Journal
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Let be a holomorphic function and a holomorphic self-map of the open unit disk in the complex plane. We provide new characterizations for the boundedness of the weighted composition operators from Zygmund type spaces to Bloch type spaces in in terms of , , their derivatives, and , the -th power of . Moreover, we obtain some similar estimates for the essential norms of the operators , from which sufficient and necessary conditions of compactness of follows immediately. ...