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New characterizations for weighted composition operator from Zygmund type spaces to Bloch type spaces

Xin-Cui Guo, Ze-Hua Zhou (2015)

Czechoslovak Mathematical Journal

Let u be a holomorphic function and ϕ a holomorphic self-map of the open unit disk 𝔻 in the complex plane. We provide new characterizations for the boundedness of the weighted composition operators u C ϕ from Zygmund type spaces to Bloch type spaces in 𝔻 in terms of u , ϕ , their derivatives, and ϕ n , the n -th power of ϕ . Moreover, we obtain some similar estimates for the essential norms of the operators u C ϕ , from which sufficient and necessary conditions of compactness of u C ϕ follows immediately.

New existence and stability results for partial fractional differential inclusions with multiple delay

Saïd Abbas, Wafaa A. Albarakati, Mouffak Benchohra, Mohamed Abdalla Darwish, Eman M. Hilal (2015)

Annales Polonici Mathematici

We discuss the existence of solutions and Ulam's type stability concepts for a class of partial functional fractional differential inclusions with noninstantaneous impulses and a nonconvex valued right hand side in Banach spaces. An example is provided to illustrate our results.

Nonabsolutely convergent series

Dana Fraňková (1991)

Mathematica Bohemica

Assume that for any t from an interval [ a , b ] a real number u ( t ) is given. Summarizing all these numbers u ( t ) is no problem in case of an absolutely convergent series ∑ t ∈ [ a , b ] u ( t ) . The paper gives a rule how to summarize a series of this type which is not absolutely convergent, using a theory of generalized Perron (or Kurzweil) integral.

Non-differentiability of Feynman paths

Pat Muldowney (2025)

Czechoslovak Mathematical Journal

A well-known mathematical property of the particle paths of Brownian motion is that such paths are, with probability one, everywhere continuous and nowhere differentiable. R. Feynman (1965) and elsewhere asserted without proof that an analogous property holds for the sample paths (or possible paths) of a non-relativistic quantum mechanical particle to which a conservative force is applied. Using the non-absolute integration theory of Kurzweil and Henstock, this article provides an introductory proof...

Nonexistence Results of Solutions of Semilinear Differential Inequalities with Temperal Fractional Derivative on the Heinsenberg Group

Haouam, K., Sfaxi, M. (2009)

Fractional Calculus and Applied Analysis

2000 Mathematics Subject Classification: 26A33, 33C60, 44A15, 35K55Denoting by Dα0|t the time-fractional derivative of order α (α ∈ (0, 1)) in the sense of Caputo, and by ∆H the Laplacian operator on the (2N + 1) - dimensional Heisenberg group H^N, we prove some nonexistence results for solutions to problems of the type Dα0|tu − ∆H(au) >= |u|^p, Dα0|tu − ∆H(au) >= |v|^p, Dδ0|tv − ∆H(bv) >= |u|^q, in H^N × R+ , with a, b ∈ L ∞ (H^N × R+). For α = 1 (and δ = 1 in the case of two inequalities),...

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