On the strong maximal function and Zygmund's class $L(log^{+} L)^{n}$

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

The Multilinear Strong Maximal Function

A multivariable version of the strong maximal function is introduced and a sharp distributional estimate for this operator in the spirit of the Jessen, Marcinkiewicz, and Zygmund theorem is obtained. Conditions that characterize the boundedness of this multivariable operator on products of weighted Lebesgue spaces equipped with multiple weights are obtained. Results for other multi(sub)linear m...

THE ROPER-SUFFRIDGE EXTENSION OPERATORS ON THE CLASS OF STRONG AND ALMOST SPIRALLIKE MAPPINGS OF TYPE $beta$ AND ORDER $alpha$

Let$mathbb{C}^n$ be the space of $n$ complex variables. Let$Omega_{n,p_2,ldots,p_n}$ be a complete Reinhardt on$mathbb{C}^n$. The Minkowski functional on complete Reinhardt$Omega_{n,p_2,ldots,p_n}$ is denoted by $rho(z)$. The concept ofspirallike mapping of type $beta$ and order $alpha$ is defined.So, the concept of the strong and almost spirallike mappings o...

A Strong Maximum Modulus Theorem for Maximal Function Algebras

Small - x behavior of the structure function F 2 and its slope ∂ ln F 2 / ∂ ln ( 1 / x ) for “ frozen ” and analytic strong - coupling constants

Using the leading-twist approximation of the Wilson operator product expansion with “frozen” and analytic versions of the strong-coupling constant, we show that the Bessel-inspired behavior of the structure function F2 and its slope ∂ lnF2/∂ ln(1/x) at small values of x, obtained for a flat initial condition in the DGLAP evolution equations, leads to good agreement with experimental data of dee...