Embedding of $$\mathcal {F}(p,p-2,s)$$ spaces into tent spaces and Volterra integral operator

The boundedness and compactness of the inclusion mapping from Besov spaces to tent spaces are studied in this paper. Meanwhile, the boundedness, compactness, and essential norm of the Volterra integral operator T g from Besov spaces to a class of general function spaces are also investigated.

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Nonlinear Evolution Equations with Exponentially Decaying Memory: Existence via Time Discretisation, Uniqueness, and Stability

Computational Methods in Applied Mathematics ◽

10.1515/cmam-2018-0268 ◽

2020 ◽

Vol 20 (1) ◽

pp. 89-108 ◽

Cited By ~ 1

Author(s):

André Eikmeier ◽

Etienne Emmrich ◽

Hans-Christian Kreusler

Keyword(s):

Banach Space ◽

Integral Operator ◽

Evolution Equations ◽

Nonlinear Evolution ◽

Nonlinear Evolution Equations ◽

Inner Product ◽

Initial Value ◽

Time Discretisation ◽

Volterra Integral Operator ◽

Stability Results

AbstractThe initial value problem for an evolution equation of type {v^{\prime}+Av+BKv=f} is studied, where {A:V_{A}\to V_{A}^{\prime}} is a monotone, coercive operator and where {B:V_{B}\to V_{B}^{\prime}} induces an inner product. The Banach space {V_{A}} is not required to be embedded in {V_{B}} or vice versa. The operator K incorporates a Volterra integral operator in time of convolution type with an exponentially decaying kernel. Existence of a global-in-time solution is shown by proving convergence of a suitable time discretisation. Moreover, uniqueness as well as stability results are proved. Appropriate integration-by-parts formulae are a key ingredient for the analysis.

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Inverse nodal problems for integro-differential operators with a constant delay

Journal of Inverse and Ill-Posed Problems ◽

10.1515/jiip-2018-0088 ◽

2019 ◽

Vol 27 (4) ◽

pp. 501-509 ◽

Cited By ~ 6

Author(s):

Murat Sat ◽

Chung Tsun Shieh

Keyword(s):

Integral Operator ◽

Potential Function ◽

Liouville Operator ◽

Differential Operators ◽

Constant Delay ◽

Nodal Points ◽

Inverse Nodal Problems ◽

Volterra Integral Operator ◽

Sturm Liouville

Abstract We study inverse nodal problems for Sturm–Liouville operator perturbed by a Volterra integral operator with a constant delay. We have estimated nodal points and nodal lengths for this operator. Moreover, by using these data, we have shown that the potential function of this operator can be established uniquely.

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Norm of a Volterra Integral Operator on Some Analytic Function Spaces

ISRN Mathematical Analysis ◽

10.1155/2013/492052 ◽

2013 ◽

Vol 2013 ◽

pp. 1-6

Author(s):

Hao Li ◽

Songxiao Li

Keyword(s):

Analytic Function ◽

Integral Operator ◽

Unit Disc ◽

Function Spaces ◽

Volterra Integral Operator ◽

Analytic Function Spaces

Let f be an analytic function in the unit disc 𝔻. The Volterra integral operator If is defined as follows: If(h)(z)=∫0zf(w)h'(w)dw,h∈H(𝔻),z∈𝔻. In this paper, we compute the norm of If on some analytic function spaces.

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