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C. Watari [12] obtained a simple characterization of Lipschitz classes $L i p^{(p)} α (W) (1 \geq p \geq \infty, α > 0)$ on the dyadic group using the $L^{p}$ -modulus of continuity and the best approximation by Walsh polynomials. Onneweer and Weiyi [4] characterized homogeneous Besov spaces $B_{p, q}^{α}$ on locally compact Vilenkin groups, but there are still some gaps to be filled up. Our purpose is to give the characterization of Besov spaces $B_{p, q}^{α}$ by oscillations, atoms and others on the dyadic groups. As applications, we show a strong capacity inequality of the...

On the characterization of harmonic functions with initial data in Morrey space

Bo Li, Jinxia Li, Bolin Ma, Tianjun Shen (2024)

Czechoslovak Mathematical Journal

Let $(X, d, μ)$ be a metric measure space satisfying the doubling condition and an $L^{2}$ -Poincaré inequality. Consider the nonnegative operator $ℒ$ generalized by a Dirichlet form on $X$ . We will show that a solution $u$ to $(- \partial_{t}^{2} + ℒ) u = 0$ on $X \times ℝ_{+}$ satisfies an $α$ -Carleson condition if and only if $u$ can be represented as the Poisson integral of the operator $ℒ$ with the trace in the generalized Morrey space $L^{2, α} (X)$ , where $α$ is a nonnegative function defined on a class of balls in $X$ . This result extends the analogous characterization founded...

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On s-sets and mutual absolute continuity of measures on homogeneous spaces.

On strictly sparse subsets of a free group.

On strong Riesz sets

On symmetry of group algebras of discrete nilpotent groups

On tails of stationary measures on a class of solvable groups

On Tensor Products of Banach Lattices.

On the Asymptotic Behaviour of Convolution Powers of Probabilities on Discrete Groups.

On the Banach algebra A (...) for smooth sets ... Rn.

On the behaviour of sequences in the dual of a nilpotent Lie group.

On the Bohr Compactification of a Transformation Group.

On the Bohr Topology in Amenable Topological Groups.

On the causal structure of Lorentzian Lie groups. A globality theorem for Lorentzian cones in certain solvable Lie algebras.

On the characterization of Hardy-Besov spaces on the dyadic group and its applications

On the characterization of harmonic functions with initial data in Morrey space

On the characterization of isotropic Gaussian fields on homogeneous spaces of compact groups.

On the characters of exponential solvable Lie groups

On the Charshiladze-Lozinski Theorem for Compact Topological Groups and Homogeneous Spaces.

On the complexity of H sets of the unit circle

On the Conjugation Representation of a Locally Compact Group.

On the construction of fundamental solutions for differential operators on nilpotent groups

Currently displaying 141 – 160 of 260