A study of exceptional sets in a finite product of Brelot spaces is made. The principal results obtained are a convergence theorem for decreasing sequences of n-superharmonic functions and an extension theorem for positive n-superharmonic functions. Similar results are obtained for plurisuperharmonic functions.

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We consider the problem of characterising Besov-Lipshitz and Triebel-Lizorkin spaces using kernels with limited smoothness and decay. This extends the work of H.-Q. Bui et al in [4] and [5] from kernels in S to more general kernels, including the Poisson kernel. We overcome the difficulty of defining the convolution of a general kernel with a distribution by using the concept of a bounded distribution introduced by E. Stein [12]. The characterisations we obtain are valid for the full range of indices.

In this work we will study Hardy-Littlewood maximal function and maximal operator, basing on both classical and most up to date works. In the first chapter we will give definitions for different types of those objects and consider some of their most important properties. The second chapter is entirely devoted to an overview of the fundamental properties of Hardy-Littlewood maximal function, which are strong (p, p) and weak (1, 1) inequalities. Here we list the most actual results on this inequalities in correspondence to the way the maximal func-tion is defined. The third chapter presents the theorem on asymptotic behavior of the lower bound of the constant in the weak-type (1, 1) inequality for the maximal function associated with cubes of Rd, then the dimension d tends to infinity. In the last chapter a method forcomputing constant c, appearing in the main theorem of chapter 3, is given. / <p>QC 20140527</p>

We say that a restriction theorem holds for a curve (gamma) (t) in (//R)('n) if for all f(epsilon) ((//R)('n)) and for some p and q, there is a constant C(,p,q) such that / (VBAR)(VBAR) f (VBAR) (,(gamma)) (VBAR)(VBAR) (,L('q)(du)) (LESSTHEQ) C(,p,q) (VBAR)(VBAR) f (VBAR)(VBAR) (,L('P)((//R)('n))). / In Chapter 1, we prove restriction theorems for non-compact plane curves with non-negative affine curvature when 1 (LESSTHEQ) p < 4/3 and / (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) / There is an analogous result for space curves in the same chapter. / The Hilbert transform along the curve (gamma) is defined by / (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) / In Chapter 2, it is shown that when (gamma) has the rapidly decreasing positive affine curvature, H(,(gamma)) is a L('P)-bounded operator for / (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI)

Thesis (M.Sc.) - Carleton University, 2006. / Includes bibliographical references (p. 41-44). Also available in electronic format on the Internet.

Thesis--Copenhagen.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1962. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves [104]-108).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1967. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliography.

Thesis (M. Eng.)--Carleton University, 1986. / Also available in electronic format on the Internet.