We study embeddings between generalised Triebel–Lizorkin–Morrey spacesε_(ϕ,p,q)^(s)(R^(d))and within the scales of further generalised Morrey smoothness spaces like N_(ϕ,p,q)^(s)(R^(d)),B_(p,q)^(s,ϕ)(R^(d))and F_(p...We study embeddings between generalised Triebel–Lizorkin–Morrey spacesε_(ϕ,p,q)^(s)(R^(d))and within the scales of further generalised Morrey smoothness spaces like N_(ϕ,p,q)^(s)(R^(d)),B_(p,q)^(s,ϕ)(R^(d))and F_(p,q)^(s,ϕ)(R^(d)).The latter have been investigated in a recent paper by the first two authors(2023),while the embeddings of the scale N_(ϕ,p,q)^(s)(R^(d))were mainly obtained in a paper of the first and last two authors(2022).Now we concentrate on the characterisation of the spacesε_(ϕ,p,q)^(s)(R^(d)).Our approach requires a wavelet characterisation of those spaces which we establish for the system of Daubechies’wavelets.Then we prove necessary and sufficient conditions for the embeddingε_(ϕ1,p1,q1)^(s1)(R^(d))→ε_(2ϕ2,p2,q2)^(s)(R^(d)).We can also provide some almost final answer to the question whenε_(ϕ,p,q)^(s)(R^(d))is embedded into C(R^(d)),complementing our recent findings in case of N_(ϕ,p,q)^(s)(R^(d)).展开更多
In the current work,we introduce the class of graded regular BiHom-Lie algebras as a natural extension of the class of graded Lie algebras,and hence of split Lie algebras.In particular,we show that an arbitrary graded...In the current work,we introduce the class of graded regular BiHom-Lie algebras as a natural extension of the class of graded Lie algebras,and hence of split Lie algebras.In particular,we show that an arbitrary graded regular BiHom-Lie algebra L can be expressed as L=U+∑_(j)I_(j),where U is a linear subspace in L_(1),1 being the neutral element of the grading group,and any I_(j)a well-described(graded)ideal of L,satisfying[I_(j),I_(k)]=0 if j≠k.Moreover,under some conditions,we characterize the simplicity of L and we show that L is the direct sum of the family of its simple(graded)ideals.展开更多
Abstract We study smoothness spaces of Morrey type on Rn and characterise in detail those situa s,r n s n tions when such spaces of type Ap,q^s,r（Rn ） or A u^sp,q（R ） are not embedded into L∞（R^n）. We can show ...Abstract We study smoothness spaces of Morrey type on Rn and characterise in detail those situa s,r n s n tions when such spaces of type Ap,q^s,r（Rn ） or A u^sp,q（R ） are not embedded into L∞（R^n）. We can show that in the so-called sub-critical, proper Morrey case their growth envelope function is always infinite which is a much stronger assertion. The same applies for the Morrey spaces Mu,p（Rn） with p 〈 u. This is the first result in this direction and essentially contributes to a better understanding of the structure of the above spaces.展开更多
We study unboundedness of smoothness Morrey spaces on bounded domains ? ? R^n in terms of growth envelopes. It turns out that in this situation the growth envelope function is finite—in contrast to the results obtain...We study unboundedness of smoothness Morrey spaces on bounded domains ? ? R^n in terms of growth envelopes. It turns out that in this situation the growth envelope function is finite—in contrast to the results obtained by Haroske et al.(2016) for corresponding spaces defined on R^n. A similar effect was already observed by Haroske et al.(2017), where classical Morrey spaces M_(u,p)(?) were investigated. We deal with all cases where the concept is reasonable and also include the tricky limiting cases. Our results can be reformulated in terms of optimal embeddings into the scale of Lorentz spaces L_(p,q)(?).展开更多
Numerical solutions of a non-Fickian diffusion equation belonging to a hyperbolic type are presented in one space dimension.The Brownian particle modelled by this diffusion equation is subjected to a symmetric periodi...Numerical solutions of a non-Fickian diffusion equation belonging to a hyperbolic type are presented in one space dimension.The Brownian particle modelled by this diffusion equation is subjected to a symmetric periodic potential whose spatial shape can be varied by a single parameter.We consider a numerical method which consists of applying Laplace transform in time;we then obtain an elliptic diffusion equation which is discretized using a finite difference method.We analyze some aspects of the convergence of the method.Numerical results for particle density,flux and mean-square-displacement(covering both inertial and diffusive regimes)are presented.展开更多
基金partially supported by the German Research Foundation(DFG)(Grant No.Ha 2794/8-1)supported by the China Scholarship Council(CSC)(Grant No.202006350058)partially supported by the Center for Mathematics of the University of Coimbra(funded by the Portuguese Government through FCT/MCTES,DOI 10.54499/UIDB/00324/2020)。
文摘We study embeddings between generalised Triebel–Lizorkin–Morrey spacesε_(ϕ,p,q)^(s)(R^(d))and within the scales of further generalised Morrey smoothness spaces like N_(ϕ,p,q)^(s)(R^(d)),B_(p,q)^(s,ϕ)(R^(d))and F_(p,q)^(s,ϕ)(R^(d)).The latter have been investigated in a recent paper by the first two authors(2023),while the embeddings of the scale N_(ϕ,p,q)^(s)(R^(d))were mainly obtained in a paper of the first and last two authors(2022).Now we concentrate on the characterisation of the spacesε_(ϕ,p,q)^(s)(R^(d)).Our approach requires a wavelet characterisation of those spaces which we establish for the system of Daubechies’wavelets.Then we prove necessary and sufficient conditions for the embeddingε_(ϕ1,p1,q1)^(s1)(R^(d))→ε_(2ϕ2,p2,q2)^(s)(R^(d)).We can also provide some almost final answer to the question whenε_(ϕ,p,q)^(s)(R^(d))is embedded into C(R^(d)),complementing our recent findings in case of N_(ϕ,p,q)^(s)(R^(d)).
基金supported by the Centre for Mathematics of the University of Coimbra(UIDB/00324/2020)funded by the Portuguese Government through FCT/MCTES+2 种基金supported by the PCI of UCA'Teoría de Lie y Teoría de Espacios de Banach'and the PAI with project number FQM298supported by the 2014-2020 ERDF Operational Programme and by the Department of Economy,Knowledge,Business and University of the Regional Government of Andalusia FEDER-UCA18-107643supported by Agencia Estatal de Investigación(Spain),grant PID2020-115155GB-I00(European FEDER support included,EU).
文摘In the current work,we introduce the class of graded regular BiHom-Lie algebras as a natural extension of the class of graded Lie algebras,and hence of split Lie algebras.In particular,we show that an arbitrary graded regular BiHom-Lie algebra L can be expressed as L=U+∑_(j)I_(j),where U is a linear subspace in L_(1),1 being the neutral element of the grading group,and any I_(j)a well-described(graded)ideal of L,satisfying[I_(j),I_(k)]=0 if j≠k.Moreover,under some conditions,we characterize the simplicity of L and we show that L is the direct sum of the family of its simple(graded)ideals.
基金partially supported by the Centre for Mathematics of the University of Coimbrathe European Regional Development Fund program COMPETEthe Portuguese Government through the FCT-Fundao para a Ciencia e Tecnologia under the project PEst-C/MAT/UI0324/2013
文摘Abstract We study smoothness spaces of Morrey type on Rn and characterise in detail those situa s,r n s n tions when such spaces of type Ap,q^s,r（Rn ） or A u^sp,q（R ） are not embedded into L∞（R^n）. We can show that in the so-called sub-critical, proper Morrey case their growth envelope function is always infinite which is a much stronger assertion. The same applies for the Morrey spaces Mu,p（Rn） with p 〈 u. This is the first result in this direction and essentially contributes to a better understanding of the structure of the above spaces.
基金supported by the project "Smoothness Morrey spaces with variable exponents" approved under the agreement "Projektbezogener Personenaustausch mit Portugal-Acoes Integradas Luso-Alems’/DAAD-CRUP"the Centre for Mathematics of the University of Coimbra (Grant No. UID/MAT/00324/2013)+1 种基金funded by the Portuguese Government through FCT/MEC and co-funded by the European Regional Development Fund through the Partnership Agreement PT2020National Science Center of Poland (Grant No. 2014/15/B/ST1/00164)
文摘We study unboundedness of smoothness Morrey spaces on bounded domains ? ? R^n in terms of growth envelopes. It turns out that in this situation the growth envelope function is finite—in contrast to the results obtained by Haroske et al.(2016) for corresponding spaces defined on R^n. A similar effect was already observed by Haroske et al.(2017), where classical Morrey spaces M_(u,p)(?) were investigated. We deal with all cases where the concept is reasonable and also include the tricky limiting cases. Our results can be reformulated in terms of optimal embeddings into the scale of Lorentz spaces L_(p,q)(?).
基金supported by the research project UTAustin/MAT/066/2008.
文摘Numerical solutions of a non-Fickian diffusion equation belonging to a hyperbolic type are presented in one space dimension.The Brownian particle modelled by this diffusion equation is subjected to a symmetric periodic potential whose spatial shape can be varied by a single parameter.We consider a numerical method which consists of applying Laplace transform in time;we then obtain an elliptic diffusion equation which is discretized using a finite difference method.We analyze some aspects of the convergence of the method.Numerical results for particle density,flux and mean-square-displacement(covering both inertial and diffusive regimes)are presented.
