D |f(z)|dμ(z) )︀1/p < ∞ and by La(D, dμ) (or La(D) for short) the subspace of the space L(D) comprising the functions that are analytic on D. If p = 2, La(D) is a Hilbert subspace of L2(D) and it is called Bergman space. Let P denote the orthogonal projector of L2(D) on La(D) (Bergman projection). Let {δn}n=0 be defined by δn = (︀ 2π ∫︀ 1 0 r 2n+1w(r) dr )︀1/2 . Then, the sequence of functions ...

Let H = −∆ + V be a Schrödinger operator on L(R) with real-valued potential V , and let H0 = −∆. If V has sufficient pointwise decay, the wave operators W± = s − limt→±∞ eitHe−itH0 are known to be bounded on L(R) for all 1 < p < ∞ if zero is not an eigenvalue or resonance. We show that if there is an s-wave resonance or an eigenvalue only at zero, then the wave operators are bounded on L(R) for...

In this paper we give conditions for the L2-boundedness of singular integrals and the weak type (1,1) of approximate identities on spaces of homogeneous type. Our main tools are Cotlar's lemma and an extension of a theorem of Z6. Introduction. The behavior of singular integrals and approximate identities as operators on the space of integrable functions, i.e. the weak type (1,1), can be investi...

in the present paper, we rst modify the concepts of weakly fuzzy boundedness, strongly fuzzy boundedness, fuzzy continuity, strongly fuzzy continuity and weakly fuzzy continuity. then, we try to nd some relations by making a comparative study of the fuzzy norms of linear operators.

A new definition of boundedness of linear order-homomorphisms (LOH)in $L$-topological vector spaces is proposed. The new definition iscompared with the previous one given by Fang [The continuity offuzzy linear order-homomorphism, J. Fuzzy Math. 5 (4) (1997)829$-$838]. In addition, the relationship between boundedness andcontinuity of LOHs is discussed. Finally, a new uniform boundednessprincipl...

Fix d≥3 and 10⁡e−tLV|f| are bounded on weighted Lebesgue space Lp(w). The boundedness LV-Riesz potentials LV−α/2 from Lp(w) Lν(wν/p) 0<α≤2, 1<p<dα 1ν=1p−αd will also b...

In Rn define (TXirf)~(£) = /(£)(! k_1í2l)+If n > 3, A > ¿(n-l)/(n+l)and2 and the associated maximal operators are r;/(x) = suP|(/-(i-Ki2)i)-|(x). r>0 It is conjectured that, when A > 0, T\ is bounded on Lp if and only if pó(A) < p < Po(A), where po(A)...

The purpose of this paper is to prove the L p (R n ; dd) boundedness, for p > 1, of the non-centered Hardy-Littlewood maximal operator associated with the Gaussian measure dd = e ?jxj 2 dx. Let dd = e ?jxj 2 dx be a Gaussian measure in Euclidean space R n. We consider the non-centered maximal function deened by Mf(x) = sup x2B 1 (B) Z B jfj dd; where the supremum is taken over all balls B in R ...