On integral operators with operator-valued kernels.

Shahmurov, Rishad

Displaying similar documents to “On integral operators with operator-valued kernels.”

Embedding operators and maximal regular differential-operator equations in Banach-valued function spaces.

Shakhmurov, Veli B. (2005)

Journal of Inequalities and Applications [electronic only]

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Strong solutions for a compressible fluid model of Korteweg type

Matthias Kotschote (2008)

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Embedding theorems in Banach-valued $B$ -spaces and maximal $B$ -regular differential-operator equations.

Shakhmurov, Veli B. (2006)

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Estimates for the commutator of bilinear Fourier multiplier

Guoen Hu, Wentan Yi (2013)

Czechoslovak Mathematical Journal

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Let $b_{1}, b_{2} \in BMO (ℝ^{n})$ and $T_{σ}$ be a bilinear Fourier multiplier operator with associated multiplier $σ$ satisfying the Sobolev regularity that ${sup}_{κ \in ℤ} {∥ σ_{κ} ∥}_{W^{s_{1}, s_{2}} (ℝ^{2 n})} < \infty$ for some $s_{1}, s_{2} \in (n / 2, n]$ . In this paper, the behavior on $L^{p_{1}} (ℝ^{n}) \times L^{p_{2}} (ℝ^{n})$ $(p_{1}, p_{2} \in (1, \infty))$ , on $H^{1} (ℝ^{n}) \times L^{p_{2}} (ℝ^{n})$ $(p_{2} \in [2, \infty))$ , and on $H^{1} (ℝ^{n}) \times H^{1} (ℝ^{n})$ , is considered for the commutator $T_{σ, \vec{b}}$ defined by $\begin{matrix} T_{σ, \vec{b}} (f_{1}, f_{2}) (x) = & b_{1} (x) T_{σ} (f_{1}, f_{2}) (x) - T_{σ} (b_{1} f_{1}, f_{2}) (x) & + b_{2} (x) T_{σ} (f_{1}, f_{2}) (x) - T_{σ} (f_{1}, b_{2} f_{2}) (x) . \end{matrix}$ By kernel estimates of the bilinear Fourier multiplier operators and employing some techniques in the theory of bilinear singular integral operators, it is proved that these mapping properties are very similar to those...

Spaces of $D_{L^{p}}$ type and a convolution product associated with the spherical mean operator.

Dziri, M., Jelassi, M., Rachdi, L.T. (2005)

International Journal of Mathematics and Mathematical Sciences

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Boundedness of some sublinear operators and commutators on Morrey-Herz spaces with variable exponents

Yan Lu, Yue Ping Zhu (2014)

Czechoslovak Mathematical Journal

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We introduce a new type of variable exponent function spaces $M {\dot{K}}_{q, p (\cdot)}^{α (\cdot), λ} (ℝ^{n})$ of Morrey-Herz type where the two main indices are variable exponents, and give some propositions of the introduced spaces. Under the assumption that the exponents $α$ and $p$ are subject to the log-decay continuity both at the origin and at infinity, we prove the boundedness of a wide class of sublinear operators satisfying a proper size condition which include maximal, potential and Calderón-Zygmund operators and their commutators...

Boundedness of the maximal, potential and singular operators in the generalized Morrey spaces.

Guliyev, Vagif S. (2009)

Journal of Inequalities and Applications [electronic only]

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On the boundedness of the maximal operator and singular integral operators in generalized Morrey spaces

Ali Akbulut, Vagif Guliyev, Rza Mustafayev (2012)

Mathematica Bohemica

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In the paper we find conditions on the pair $(ω_{1}, ω_{2})$ which ensure the boundedness of the maximal operator and the Calderón-Zygmund singular integral operators from one generalized Morrey space $ℳ_{p, ω_{1}}$ to another $ℳ_{p, ω_{2}}$ , $1 < p < \infty$ , and from the space $ℳ_{1, ω_{1}}$ to the weak space $W ℳ_{1, ω_{2}}$ . As applications, we get some estimates for uniformly elliptic operators on generalized Morrey spaces.