The max norm in -isometries and measure
Regina Cohen, James W. Fickett (1982)
Colloquium Mathematicae
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Regina Cohen, James W. Fickett (1982)
Colloquium Mathematicae
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Ross Stokke (2022)
Commentationes Mathematicae Universitatis Carolinae
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We show how the measure theory of regular compacted-Borel measures defined on the -ring of compacted-Borel subsets of a weighted locally compact group provides a compatible framework for defining the corresponding Beurling measure algebra , thus filling a gap in the literature.
Ming-Yi Lee (2012)
Studia Mathematica
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Let w be in the Muckenhoupt weight class. We show that the Riesz transforms are bounded on the weighted Carleson measure space , the dual of the weighted Hardy space , 0 < p ≤ 1.
Ryotaro Sato (2004)
Colloquium Mathematicae
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Let X be a reflexive Banach space and (Ω,,μ) be a probability measure space. Let T: M(μ;X) → M(μ;X) be a linear operator, where M(μ;X) is the space of all X-valued strongly measurable functions on (Ω,,μ). We assume that T is continuous in the sense that if (fₙ) is a sequence in M(μ;X) and in measure for some f ∈ M(μ;X), then also in measure. Then we consider the functional equation f = (T-I)h, where f ∈ M(μ;X) is given. We obtain several conditions for the existence of h ∈ M(μ;X)...
Yu Deng (2015)
Journal of the European Mathematical Society
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In this paper we consider the periodic Benjemin-Ono equation.We establish the invariance of the Gibbs measure associated to this equation, thus answering a question raised in Tzvetkov [28]. As an intermediate step, we also obtain a local well-posedness result in Besov-type spaces rougher than , extending the well-posedness result of Molinet [20].
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.
Luis Bernal-González (2010)
Studia Mathematica
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We provide sharp conditions on a measure μ defined on a measurable space X guaranteeing that the family of functions in the Lebesgue space (p ≥ 1) which are not q-integrable for any q > p (or any q < p) contains large subspaces of (without zero). This improves recent results due to Aron, García, Muñoz, Palmberg, Pérez, Puglisi and Seoane. It is also shown that many non-q-integrable functions can even be obtained on any nonempty open subset of X, assuming that X is a topological...
Guoen Hu, Dachun Yang (2008)
Studia Mathematica
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Let μ be a nonnegative Radon measure on which satisfies μ(B(x,r)) ≤ Crⁿ for any and r > 0 and some positive constants C and n ∈ (0,d]. In this paper, some weighted norm inequalities with weights of Muckenhoupt type are obtained for maximal singular integral operators with such a measure μ, via certain weighted estimates with weights of Muckenhoupt type involving the John-Strömberg maximal operator and the John-Strömberg sharp maximal operator, where ϱ,p ∈ [1,∞).
Gogi Pantsulaia (2009)
Bulletin of the Polish Academy of Sciences. Mathematics
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New concepts of Lebesgue measure on are proposed and some of their realizations in the ZFC theory are given. Also, it is shown that Baker’s both measures [1], [2], Mankiewicz and Preiss-Tišer generators [6] and the measure of [4] are not α-standard Lebesgue measures on for α = (1,1,...).
Liang Zhang, Hui-Qiang Lu, Xiao-Mei Fu, Ze-Hua Zhou (2017)
Czechoslovak Mathematical Journal
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Let be a locally compact group and let Recently, Chen et al. characterized hypercyclic, supercyclic and chaotic weighted translations on locally compact groups and their homogeneous spaces. There has been an increasing interest in studying the disjoint hypercyclicity acting on various spaces of holomorphic functions. In this note, we will study disjoint hypercyclic and disjoint supercyclic powers of weighted translation operators on the Lebesgue space in terms of the weights. Sufficient...
S. Lasher (1968)
Studia Mathematica
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Anders Johansson, Anders Öberg, Mark Pollicott (2012)
Journal of the European Mathematical Society
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We improve and subsume the conditions of Johansson and Öberg and Berbee for uniqueness of a -measure, i.e., a stationary distribution for chains with complete connections. In addition, we prove that these unique -measures have Bernoulli natural extensions. We also conclude that we have convergence in the Wasserstein metric of the iterates of the adjoint transfer operator to the -measure.
Eric Amar (2008)
Annales Polonici Mathematici
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Let S be a sequence of points in the unit ball of ℂⁿ which is separated for the hyperbolic distance and contained in the zero set of a Nevanlinna function. We prove that the associated measure is bounded, by use of the Wirtinger inequality. Conversely, if X is an analytic subset of such that any δ -separated sequence S has its associated measure bounded by C/δⁿ, then X is the zero set of a function in the Nevanlinna class of . As an easy consequence, we prove that if S is a dual...
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 ≤ ∞.
Stanisław Bylka, Jan Komar (2007)
Discussiones Mathematicae Graph Theory
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This paper deals with weighted set systems (V,,q), where V is a set of indices, and the weight q is a nonnegative integer function on . The basic idea of the paper is to apply weighted set systems to formulate restrictions on intersections. It is of interest to know whether a weighted set system can be represented by set intersections. An intersection representation of (V,,q) is defined to be an indexed family of subsets of a set S such that for each E ∈ . A necessary condition...
Abdessatar Barhoumi, Habib Ouerdiane, Anis Riahi (2007)
Banach Center Publications
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he paper is devoted to investigation of Gegenbauer white noise functionals. A particular attention is paid to the construction of the infinite dimensional Gegenbauer white noise measure , via the Bochner-Minlos theorem, on a suitable nuclear triple. Then we give the chaos decomposition of the L²-space with respect to the measure by using the so-called β-type Wick product.
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.
Wojciech M. Zajączkowski (2010)
Applicationes Mathematicae
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The existence of solutions to the elliptic problem rot v = w, div v = 0 in a bounded domain Ω ⊂ ℝ³, , S = ∂Ω in weighted -Sobolev spaces is proved. It is assumed that an axis L crosses Ω and the weight is a negative power function of the distance to the axis. The main part of the proof is devoted to examining solutions of the problem in a neighbourhood of L. The existence in Ω follows from the technique of regularization.
Chin-Cheng Lin, Kunchuan Wang (2012)
Studia Mathematica
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We study Calderón-Zygmund operators acting on generalized Carleson measure spaces and show a necessary and sufficient condition for their boundedness. The spaces are a generalization of BMO, and can be regarded as the duals of homogeneous Triebel-Lizorkin spaces as well.
Michał Morayne (1987)
Colloquium Mathematicae
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Michael Lacey (2011)
Banach Center Publications
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For an L²-bounded Calderón-Zygmund Operator T acting on , and a weight w ∈ A₂, the norm of T on L²(w) is dominated by . The recent theorem completes a line of investigation initiated by Hunt-Muckenhoupt-Wheeden in 1973 (MR0312139), has been established in different levels of generality by a number of authors over the last few years. It has a subtle proof, whose full implications will unfold over the next few years. This sharp estimate requires that the A₂ character of the weight can...
Andrea R. Nahmod, Tadahiro Oh, Luc Rey-Bellet, Gigliola Staffilani (2012)
Journal of the European Mathematical Society
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We construct an invariant weighted Wiener measure associated to the periodic derivative nonlinear Schrödinger equation in one dimension and establish global well-posedness for data living in its support. In particular almost surely for data in a Fourier–Lebesgue space with and scaling like , for small . We also show the invariance of this measure.
Yu-Xia Liang, Chang-Jin Wang, Ze-Hua Zhou (2015)
Annales Polonici Mathematici
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Let H() denote the space of all holomorphic functions on the unit ball ⊂ ℂⁿ. Let φ be a holomorphic self-map of and u∈ H(). The weighted composition operator on H() is defined by . We investigate the boundedness and compactness of induced by u and φ acting from Zygmund spaces to Bloch (or little Bloch) spaces in the unit ball.
Ajay K. Sharma, S. Ueki (2012)
Annales Polonici Mathematici
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We characterize compact composition operators acting on weighted Bergman-Orlicz spaces , where α > -1 and ψ is a strictly increasing, subadditive convex function defined on [0,∞) and satisfying ψ(0) = 0, the growth condition and the Δ₂-condition. In fact, we prove that is compact on if and only if it is compact on the weighted Bergman space .
Uffe Haagerup, Hanne Schultz (2009)
Publications Mathématiques de l'IHÉS
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Let ℳ be a von Neumann factor of type II1 with a normalized trace τ. In 1983 L. G. Brown showed that to every operator T∈ℳ one can in a natural way associate a spectral distribution measure μ T (now called the Brown measure of T), which is a probability measure in ℂ with support in the spectrum σ(T) of T. In this paper it is shown that for every T∈ℳ and every Borel set B in ℂ, there is a unique closed T-invariant subspace affiliated with ℳ, such that the Brown measure of is concentrated...
G. Pantsulaia (2004)
Bulletin of the Polish Academy of Sciences. Mathematics
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An example of a nonzero σ-finite Borel measure μ with everywhere dense linear manifold of admissible (in the sense of invariance) translation vectors is constructed in the Hilbert space ℓ₂ such that μ and any shift of μ by a vector are neither equivalent nor orthogonal. This extends a result established in [7].