ENDPOINT MAPPING PROPERTIES OF SPHERICAL MAXIMAL OPERATORS

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

Spherical Maximal Operators on Radial Functions

where dσ is the rotationally invariant measure on Sd−1, normalized such that σ(Sd−1) = 1. Stein [5] showed that limt→0Atf(x) = f(x) almost everywhere, provided f ∈ L(R), p > d/(d − 1) and d ≥ 3. Later Bourgain [1] extended this result to the case d = 2. If p ≤ d/(d − 1) then pointwise convergence fails. However if {tj}j=1 is a fixed sequence converging to 0 then pointwise convergence may hold f...

Stronger Maximal Monotonicity Properties of Linear Operators

On two properties of enlargements of maximal monotone operators

We give an answer to an open problem regarding the full enlargeability of a maximal monotone operator S : X ⇒ X∗ by Sse, the smallest enlargement belonging to a certain class of enlargements associated to S. Moreover, we prove the weak∗ closedness of the set ShS (ε1, x)+ThT (ε2, x) under a weak generalized interior regularity condition.

An endpoint estimate for the Kunze - Stein phenomenon and related maximal operators

One of the purposes of this paper is to prove that if G is a noncompact connected semisimple Lie group of real rank one with finite center, then L(G) ∗ L(G) ⊆ L(G). Let K be a maximal compact subgroup of G and X = G/K a symmetric space of real rank one. We will also prove that the noncentered maximal operator M2f(z) = sup z∈B 1 |B| ∫ B |f(z)| dz is bounded from L2,1(X) to L2,∞(X) and from Lp(X)...