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Fractional multilinear integrals with rough kernels on generalized weighted Morrey spaces

Ali Akbulut, Amil Hasanov (2016)

Open Mathematics

In this paper, we study the boundedness of fractional multilinear integral operators with rough kernels [...] TΩ,αA1,A2,…,Ak, T Ω , α A 1 , A 2 , ... , A k , which is a generalization of the higher-order commutator of the rough fractional integral on the generalized weighted Morrey spaces Mp,ϕ (w). We find the sufficient conditions on the pair (ϕ1, ϕ2) with w ∈ Ap,q which ensures the boundedness of the operators [...] TΩ,αA1,A2,…,Ak, T Ω , α A 1 , A 2 , ... , A k , from [...] Mp,φ1wptoMp,φ2wq M p , ϕ 1 w p to M p , ϕ 2 w q for 1 < p < q < ∞. In all cases the conditions for...

Fractional Powers of Almost Non-Negative Operators

Martínez, Celso, Sanz, Miguel, Redondo, Antonia (2005)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: Primary 47A60, 47D06.In this paper, we extend the theory of complex powers of operators to a class of operators in Banach spaces whose spectrum lies in C ]−∞, 0[ and whose resolvent satisfies an estimate ||(λ + A)(−1)|| ≤ (λ(−1) + λm) M for all λ > 0 and for some constants M > 0 and m ∈ R. This class of operators strictly contains the class of the non negative operators and the one of operators with polynomially bounded resolvent. We also prove that this theory...

Fractional powers of operators, K-functionals, Ulyanov inequalities

Walter Trebels, Ursula Westphal (2010)

Banach Center Publications

Given an equibounded (₀)-semigroup of linear operators with generator A on a Banach space X, a functional calculus, due to L. Schwartz, is briefly sketched to explain fractional powers of A. Then the (modified) K-functional with respect to ( X , D ( ( - A ) α ) ) , α > 0, is characterized via the associated resolvent R(λ;A). Under the assumption that the resolvent satisfies a Nikolskii type inequality, | | λ R ( λ ; A ) f | | Y ≤ c φ ( 1 / λ ) | | f | | X , for a suitable Banach space Y, an Ulyanov inequality is derived. This will be of interest if one has good control...

Fragmentation-Coagulation Models of Phytoplankton

Ryszard Rudnicki, Radosław Wieczorek (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

We present two new models of the dynamics of phytoplankton aggregates. The first one is an individual-based model. Passing to infinity with the number of individuals, we obtain an Eulerian model. This model describes the evolution of the density of the spatial-mass distribution of aggregates. We show the existence and uniqueness of solutions of the evolution equation.

Frames associated with expansive matrix dilations.

Kwok-Pun Ho (2003)

Collectanea Mathematica

We construct wavelet-type frames associated with the expansive matrix dilation on the Anisotropic Triebel-Lizorkin spaces. We also show the a.e. convergence of the frame expansion which includes multi-wavelet expansion as a special case.

Fréchet interpolation spaces and Grothendieck operator ideals.

Jesús M. Fernández Castillo (1991)

Collectanea Mathematica

Starting with a continuous injection I: X → Y between Banach spaces, we are interested in the Fréchet (non Banach) space obtained as the reduced projective limit of the real interpolation spaces. We study relationships among the pertenence of I to an operator ideal and the pertenence of the given interpolation space to the Grothendieck class generated by that ideal.

Fredholm determinants

Henry McKean (2011)

Open Mathematics

The article provides with a down to earth exposition of the Fredholm theory with applications to Brownian motion and KdV equation.

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