The natural BMO (bounded mean oscillation) conditions suggested by scalar-valued results are known to be insufficient for the boundedness of operator-valued paraproducts. Accordingly, singular integrals has only been available under versions classical “T(1)?BMO” assumptions that not easily checkable. Recently, Hong, Liu and Mei (J. Funct. Anal. 2020) observed situation improves remarkably with ...

Vector-valued elliptic and parabolic boundary value problems subject to general boundary conditions have been investigated recently in [DHP01] in the Lp-context for 1 < p < 1. One of the main goals of this paper was to deduce a maximal Lp-regularity result for the solution of the parabolic initial boundary value problem. A classical reference in the elliptic context are the celebrated papers of...

We introduce lower and upper limits of vector-valued functions with respect to the usual positive cone in a finite-dimensional space. Using these concepts, we extend the definitions ofm-th order lower and upper directional derivatives introduced in Studniarski (1986) [1] to vector-valued functions, and prove some necessary and sufficient conditions for strict local Pareto minimizers of orderm. ...

We study the space of all continuous fuzzy-valued functions  from a space $X$ into the space of fuzzy numbers $(mathbb{E}sp{1},dsb{infty})$  endowed with the pointwise convergence topology.   Our results generalize the classical ones for  continuous real-valued functions.   The field of applications of this approach seems to be large, since the classical case  allows many known devices to be fi...

We consider the problem of minimizing the distance ‖f − φ‖Lp(K), where K is a subset of the complex unit circle ∂D and φ ∈ C(K), subject to the constraint that f lies in the Hardy space H(D) and |f | ≤ g for some positive function g. This problem occurs in the context of filter design for causal LTI systems. We show that the optimization problem has a unique solution, which satisfies an extrema...

In this paper, we define a new cosine similarity between two interval valued neutrosophic sets based on Bhattacharya’s distance [19]. The notions of interval valued neutrosophic sets (IVNS, for short) will be used as vector representations in 3D-vector space. Based on the comparative analysis of the existing similarity measures for IVNS, we find that our proposed similarity measure is better an...

In this paper, we define a new cosine similarity between two interval valued neutrosophic sets based on Bhattacharya’s distance [19]. The notions of interval valued neutrosophic sets (IVNS, for short) will be used as vector representations in 3D-vector space. Based on the comparative analysis of the existing similarity measures for IVNS, we find that our proposed similarity measure is better an...

In this paper, we derive certain algebraic properties of Toeplitz and Hankel operators defined on the vector-valued Bergman spaces L2,C n a (D), where D is the open unit disk in C and n ≥ 1. We show that the set of all Toeplitz operators TΦ,Φ ∈ LMn(D) is strongly dense in the set of all bounded linear operators L(L2,Cn a (D)) and characterize all finite rank little Hankel operators.

We give the matrix characterizations from Nakano vector-valued sequence space (X,p) and Fr (X,p) into the sequence spaces Er , ∞, ∞(q), bs, and cs, where p = (pk) and q = (qk) are bounded sequences of positive real numbers such that pk > 1 for all k∈N and r ≥ 0. 2000 Mathematics Subject Classification. 46A45.

We apply Preuss' concept of $mbbe$-connectedness to the categories of lattice-valued uniform convergence spaces and of lattice-valued uniform spaces. A space is uniformly $mbbe$-connected if the only uniformly continuous mappings from the space to a space in the class $mbbe$ are the constant mappings. We develop the basic theory for $mbbe$-connected sets, including the product theorem. Furtherm...