A generalization of the boundedness of certain integral operators in variable lebesgue spaces

Let n ε N. Let A1, ...Am be n×n invertible matrices. Let 0 ≤ α < n and 0 < αi < n such that α1 +...+αm = n-α . We define In [8] we obtained the boundedness of this operator from Lp(.)(Rn) into Lq(.)(Rn) for 1/q(.) = 1/p(.) - α/n, in the case that Ai is a power of certain fixed matrix A and for exponent functions p satisfying log-Hölder conditions and p(Ay) = p(y), y ε Rn. We will show now that the hypothesis on p, in certain cases, is necessary for the boundedness of Tα and we also prove the result for more general matrices Ai.Fil: Urciuolo, Marta. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Vallejos, Lucas Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentin

Integral operators with rough kernels in variable Lebesgue spaces

We study integral operators with kernels K(x, y) = k1(x- A1y) ⋯ km(x- Amy) , ki(x)=Ωi(x)|x|n/qi where Ω i: Rn→ R are homogeneous functions of degree zero,satisfying a size and a Dini condition, Ai are certain invertible matrices, andnq1+⋯+nqm=n-α,0≤αFil: Urciuolo, Marta. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Vallejos, Lucas Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentin

Weighted inequalities for integral operators with some homogeneous kernels

summary:In this paper we study integral operators of the form $$Tf(x)=\int | x-a_1y|^{-\alpha _1}\dots | x-a_my|^{-\alpha _m}f(y)\mathrm{d}y,$$ $\alpha _1+\dots +\alpha _m=n$. We obtain the $L^p(w)$ boundedness for them, and a weighted $(1,1)$ inequality for weights $w$ in $A_p$ satisfying that there exists $c\ge 1$ such that $w( a_ix) \le cw( x)$ for a.e. $x\in \mathbb R^n$, $1\le i\le m$. Moreover, we prove $\Vert Tf\Vert _{{\mathrm BMO}}\le c\Vert f\Vert _\infty$ for a wide family of functions $f\in L^\infty ( \mathbb R^n)$

L p(·)–L q(·) boundedness of some integral operators obtained by extrapolation techniques

Given a matrix A such that AM = I and 0 ≤ α < n, for an exponent p satisfying p(Ax) = p(x) for a.e. x ∈ Rn, using extrapolation techniques,we obtain Lp(·) → Lq(·) boundedness, 1/q(·) = 1/p(·) - α/n, andweak type estimates for integral operators of the form Tαf(x) = ∫ f(y)|x - A1y|α1⋯|x - Amy|αm dy, where A1,⋯, Am are different powers of A such that Ai - Aj is invertible for i ≠ j, α1 + ⋯ + αm = n - α. We give some generalizations of these results.Fil: Urciuolo, Marta. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Vallejos, Lucas Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentin

THE INFLUENCE OF PARTICLE ATTRITION ON SORBENT INVENTORY AND PARTICLE SIZE DISTRIBUTION IN AIR-BLOWN CIRCULATING FLUIDIZED BED COMBUSTORS

This paper presents a population balance model aiming at the prediction of sorbent inventory and particle size distribution establishing at steady state in the bed of an air-blown circulating fluidized bed combustor fuelled with a sulphur-bearing solid fuel. The core of the model is represented by population balance equations on sorbent particles which embody terms expressing the extent/rate of sorbent attrition/fragmentation. The effect of the progress of sulphation on attrition and fragmentation is taken into account by selection of appropriate constitutive equations. Model results are presented and discussed with the aim of clarifying the influence of particle attrition/fragmentation on sorbent inventory and particle size distribution, partitioning of sorbent between fly and bottom ash, sulphur capture efficiency. A sensitivity analysis is carried out with reference to relevant operational parameters of the combustor

Sulfur Uptake by Limestone-Based Sorbent Particles in CFBC: The Influence of Attrition/Fragmentation on Sorbent Inventory and Particle Size Distribution

This paper presents a population balance model aiming at the prediction of sorbent inventory and particle size distribution establishing at steady state in the bed of an air-blown CFBC fuelled with a sulphur-bearing solid fuel. The core of the model is represented by population balance equations on sorbent particles which embody terms expressing the extent/rate of sorbent attrition/fragmentation. The effect of the progress of sulphation on attrition and fragmentation is taken into account by selection of appropriate constitutive equations. Model results are presented and discussed with the aim of clarifying the influence of particle attrition/fragmentation on sorbent inventory and particle size distribution, partitioning of sorbent between fly and bottom ash, sulphur capture efficiency. A sensitivity analysis is carried out with reference to relevant operational parameters of the combustor

Integrales singulares sobre superficies rectificables

Fil:Urciuolo, Marta Susana. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina