The purpose of this paper is to study the endpoint boundedness properties of some multilinear operators related to certain integral operators on Herz and Herz type Hardy Spaces. The operators include Littlewood-Paley operator and Marcinkiewicz operator.

In previous work we established a multilinear duality and factorisation theory for norm inequalities pointwise weighted geometric means of positive linear operators defined on normed lattices. this paper extend the reach first time to setting general spaces. The scope includes Fourier restriction-type inequalities. We also sharpen our operators. Our results all share common theme: estimates mea...

in this paper we develop a natural generalization of schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. we prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. we prove that the operators of a dual ov-basis are continuous. we also dene the concepts of bessel, hilbert ov-basis and obt...

We show that every inner divisor of the operator-valued coordinate function, zIE, is a Blaschke-Potapov factor. also introduce notion “rational” function and then Δ two-sided rational if only it can be represented as finite product; this extends to functions well-known result proved by V.P. Potapov for matrix-valued functions.

As the development of singular integral operators, their commutators and multilinear operators have been well studied (see [3]–[7], [18]–[20]). Let T be the Calderón-Zygmund singular integral operator and b ∈ BMO(R), a classical result of Coifman, Rochberg and Weiss (see [6]) stated that the commutator [b, T ](f) = T (bf)− bT (f) is bounded on L(R) for 1 < p <∞. The purpose of this paper is to ...