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The boundedness of multilinear commutators of Calderón-Zygmund operator T... on generalized weighted Morrey spaces Mp,φ(w) with the weight function w belonging to Muckenhoupt's class Ap is studied. When 1 < p < ∞ and ... = (b1,..., bm), bi ∈ BMO, i = 1,..., m, the sufficient conditions on the pair (φ1, φ2) which ensure the boundedness of the operator T... from Mp,φ1 (w) to Mp,φ2 (w) are found. In all cases the conditions for the boundedness of T... are given in terms of Zygmund-type integral inequalities on ((φ 1,φ2), which do not assume any assumption on monotonicity of φ1 (x, r), φ2 (x,r) in r. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to discuss the boundedness properties of multilinear Calderón-Zygmund operator and its commutator on the generalized weighted Morrey spaces. [ABSTRACT FROM AUTHOR]

We will obtain the strong type and weak type estimates of intrinsic square functions including the Lusin area integral, Littlewood-Paley 퓖-function and 퓖*λ-function on the weighted Herz spaces ...α, pq(w1, w2) (Kα,pq(w1, w2)) with general weights. [ABSTRACT FROM AUTHOR]

Spaces with variable exponents Lp(x) H, μ) and Lp(x) (H, μ H) are introduced. After discussing some approximation results of Lp(x) (H, μ), Sobolev spaces on H with variable exponents are introduced. At last, we define Malliavin derivatives in Lp(x) (H, μ) and discuss some properties of Malliavin derivatives in Lp(x)(H, μ). [ABSTRACT FROM AUTHOR]

We introduce a new space QK(∂ ⅅ) of Lebesgue measurable functions on the unit circle connecting closely with the Sobolev space. We obtain a necessary and sufficient condition on K such that QK(∂ ⅅ) = BMO(∂ ⅅ), as well as a general criterion on weight functions K1 and K2, K1 ≤ K2, such that QK (∂ ⅅ) ... QK (∂ ⅅ). We also prove that a measurable function belongs to QK(∂ ⅅ) if and only if it is Mobius bounded in the Sobolev space L²K(∂ ⅅ). Finally, we obtain a dyadic characterization of functions in QK spaces in terms of dyadic arcs on the unit circle. [ABSTRACT FROM AUTHOR]

We make use of the theory of strongly continuous solution operators for fractional models together with the subordination principle for fractional evolution equations (Bazhlekova (2000) and Pruss (1993)) to analyze and show existence results for a fractional fragmentation model with growth characterized by its growth rate r. Indeed, strange phenomena like the phenomenon of shattering (McGrady and Ziff (1987)) and the sudden appearance of infinite number of particles in some systems with initial finite particles number could not be fully explained by classical models of fragmentation or aggregation. Then, there is an increasing volition to try new approaches and extend classical models to fractional ones. In the growth model, one of the major challenges in the analysis occurs when l/r(x) is integrable at x0 ≥ 0, the minimum size of a cell. We restrict our analysis to the case of integrability of r-1 at x0. This case needs more considerations on the boundary condition, which, in this paper, is the McKendrick-von Foerster renewal condition. In the process, some properties of Mittag-Leffler relaxation function Berberan-Santos (2005) are exploited to finally prove that there is a positive solution operator to the full model. [ABSTRACT FROM AUTHOR]

We study the spaces w0p, and w∞p of sequences that are strongly summable to 0, summable, and bounded with index p ≥ 1 by the Cesaro method of order 1 and establish the representations of the general bounded linear operators from the spaces wp into the spaces w∞p, w¹ and w0¹ We also give estimates for the operator norm and the Hausdorff measure of noncompactness of such operators. Finally we apply our results to characterize the classes of compact bounded linear operators from w0p and wp into w0¹ and w¹. [ABSTRACT FROM AUTHOR]

If X is a completely regular space, first we characterize those spaces Cb(X) whose compact sets are metrizable. Then we use this result to provide a general condition for X to ensure themetrizability of compact sets in Cb(X). Finally, we characterize those spaces Cb(X) that have a 픊-basis. [ABSTRACT FROM AUTHOR]

We prove the boundedness of the intrinsic functions on generalized weighted Morrey spaces Mp,φ (w), including the strong type estimates and weak type estimates. Moreover, we define the kth-order commutators generated by BMO(8477;n) functions and intrinsic functions, and obtain their strong type estimates on Mp,φ (w). In some cases, we improve previous results. [ABSTRACT FROM AUTHOR]

We obtain the boundedness of a commutator generated by multilinear Calderón-Zygmund operator and BMO functions in Herz-Morrey spaces with variable exponents. [ABSTRACT FROM AUTHOR]

We study the boundedness properties of the Fourier multiplier operator eiμ(D) on α-modulation spaces Mp,qs,α (0 ≤ α < 1) and Besov spaces Bp,qsMp,qs,1. We improve the conditions for the boundedness of Fourier multipliers with compact supports and for the boundedness of eiμ(D) on Mp,qs,α. If μ is a radial function ø (|ξ|) and ø satisfies some size condition, we obtain the sufficient and necessary conditions for the boundedness of between ... and .... [ABSTRACT FROM AUTHOR]