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Measure-geometric Laplacians for partially atomic measures

Marc Kesseböhmer, Tony Samuel, Hendrik Weyer (2020)

Commentationes Mathematicae Universitatis Carolinae

Motivated by the fundamental theorem of calculus, and based on the works of W. Feller as well as M. Kac and M. G. Kreĭn, given an atomless Borel probability measure $η$ supported on a compact subset of $ℝ$ U. Freiberg and M. Zähle introduced a measure-geometric approach to define a first order differential operator $\nabla_{η}$ and a second order differential operator $Δ_{η}$ , with respect to $η$ . We generalize this approach to measures of the form $η : = ν + δ$ , where $ν$ is non-atomic and $δ$ is finitely supported. We determine analytic...

Möbius invariance of analytic Besov spaces in tube domains over symmetric cones

G. Garrigós (2010)

Colloquium Mathematicae

Besov spaces of holomorphic functions in tubes over cones have been recently defined by Békollé et al. In this paper we show that Besov p-seminorms are invariant under conformal transformations of the domain when n/r is an integer, at least in the range 2-r/n < p ≤ ∞.

Modulation space estimates for multilinear pseudodifferential operators

Árpád Bényi, Kasso A. Okoudjou (2006)

Studia Mathematica

We prove that for symbols in the modulation spaces $ℳ^{p, q}$ , p ≥ q, the associated multilinear pseudodifferential operators are bounded on products of appropriate modulation spaces. In particular, the symbols we study here are defined without any reference to smoothness, but rather in terms of their time-frequency behavior.

Modulation space estimates for Schrödinger type equations with time-dependent potentials

Wei Wei (2014)

Czechoslovak Mathematical Journal

We give a new representation of solutions to a class of time-dependent Schrödinger type equations via the short-time Fourier transform and the method of characteristics. Moreover, we also establish some novel estimates for oscillatory integrals which are associated with the fractional power of negative Laplacian ${(- Δ)}^{κ / 2}$ with $1 \leq κ \leq 2$ . Consequently the classical Hamiltonian corresponding to the previous Schrödinger type equations is studied. As applications, a series of new boundedness results for the corresponding...

Molecules in coorbit spaces and boundedness of operators

Karlheinz Gröchenig, Mariusz Piotrowski (2009)

Studia Mathematica

We study the notion of molecules in coorbit spaces. The main result states that if an operator, originally defined on an appropriate space of test functions, maps atoms to molecules, then it can be extended to a bounded operator on coorbit spaces. For time-frequency molecules we recover some boundedness results on modulation spaces, for time-scale molecules we obtain the boundedness on homogeneous Besov spaces.

Monotonic rearrangements of functions with small mean oscillation

Dmitriy M. Stolyarov, Vasily I. Vasyunin, Pavel B. Zatitskiy (2015)

Studia Mathematica

We obtain sharp bounds for the monotonic rearrangement operator from "dyadic-type" classes to "continuous" ones; in particular, for the BMO space and Muckenhoupt classes. The idea is to connect the problem with a simple geometric construction named α-extension.

Multilinear almost diagonal estimates and applications

Árpád Bényi, Nikolaos Tzirakis (2004)

Studia Mathematica

We prove that an almost diagonal condition on the (m + 1)-linear tensor associated to an m-linear operator implies boundedness of the operator on products of classical function spaces. We then provide applications to the study of certain singular integral operators.

Multilinear analysis on metric spaces [Book]

Loukas Grafakos, Liguang Liu, Diego Maldonado, Dachun Yang (2014)

Multilinear Riesz potential on Morrey-Herz spaces with non-doubling measures.

Shi, Yanlong, Tao, Xiangxing, Zheng, Taotao (2010)

Journal of Inequalities and Applications [electronic only]

Multi-Morrey spaces for non-doubling measures

Suixin He (2019)

Czechoslovak Mathematical Journal

The spaces of multi-Morrey type for positive Radon measures satisfying a growth condition on $ℝ^{d}$ are introduced. After defining the spaces, we investigate the multilinear maximal function, the multilinear fractional integral operator and the multilinear Calderón-Zygmund operators, respectively, from multi-Morrey spaces to Morrey spaces.

Multipliers and operators on the tempered ultradistribution spaces of Roumieu type for the distributional Hankel-type transformation spaces.

Banerji, P.K., Al-Omari, S.K. (2006)

International Journal of Mathematics and Mathematical Sciences

Musielak-Orlicz-Hardy Spaces Associated with Operators Satisfying Reinforced Off-Diagonal Estimates

The Anh Bui, Jun Cao, Luong Dang Ky, Dachun Yang, Sibei Yang (2013)

Analysis and Geometry in Metric Spaces

Let X be a metric space with doubling measure and L a one-to-one operator of type ω having a bounded H∞ -functional calculus in L2(X) satisfying the reinforced (pL; qL) off-diagonal estimates on balls, where pL ∊ [1; 2) and qL ∊ (2;∞]. Let φ : X × [0;∞) → [0;∞) be a function such that φ (x;·) is an Orlicz function, φ(·;t) ∊ A∞(X) (the class of uniformly Muckenhoupt weights), its uniformly critical upper type index l(φ) ∊ (0;1] and φ(·; t) satisfies the uniformly reverse Hölder inequality of order...

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