Download Algebraic Geometry Bucharest 1982. Proc. conf by L. Badescu, D. Popescu PDF

By L. Badescu, D. Popescu

ISBN-10: 3540129308

ISBN-13: 9783540129301

Show description

Read or Download Algebraic Geometry Bucharest 1982. Proc. conf PDF

Best geometry and topology books

Symplectic Geometry & Mirror Symmetry

Court cases of the 4th KIAS Annual overseas convention, held in August 14-18, 2000, Seoul, South Korea. best specialists within the box discover the newer advancements with regards to homological reflect symmetry, Floer idea, D-branes and Gromov-Witten invariants.

General topology and applications: proceedings of the 1988 Northeast conference

Complaints of the Northeast convention at the topic at Wesleyan college, Connecticut, in June 1988. the 2 dozen papers, by means of mathematicians from the U.S., Canada, and the Netherlands, document on fresh advances in topology for examine mathematicians and graduate scholars. They specialise in the theor

Additional resources for Algebraic Geometry Bucharest 1982. Proc. conf

Example text

Next, we check (i) and (ii). (i) For the first inequality, let q ∈ (0, min{2, p}]. Clearly, the inequality is valid for p = q = 2. So we just consider following two cases. Case 1: 0 < q < 2 < p. 4. Mixture of Derivative and Quotient 37 thereupon producing F pHp I(F ; p, q). Case 2: 0 < q < p < 2. By the first Littlewood–Paley inequality above, H¨older’s inequality and the Hardy–Stein identity for Fr , we find p Hp Fr I(Fr ; p, p) I(Fr ; p, q) I(F ; p, q) 2−p 2−q 2−p 2−q I(Fr ; p, 2) Fr p(p−q) 2−q Hp p−q 2−q , thereupon implying F pHp I(F ; p, q).

22(p+q)n (1 − |w|2 )p Thus ∞ µ CMp ,q ≤ sup w∈D n=1 ∞ sup w∈D n=1 En \En−1 µ(En ) 22n(p+q) (1 − |w|2 )p ∞ µ (1 − |w|2 )q dµ(z) |1 − wz| ¯ p+q CMp 2−nq , n=1 as desired. For a, b > 0 we define formally a Ta,b operator; that is, the following integral operator: (1 − |w|2 )b−1 Ta,b f (z) = f (w)dm(w), z ∈ D. ¯ a+b D |1 − wz| In the next result we show that CMp is invariant under Ta,b . 2. Let p ∈ (0, 2), a > 2−p 2 , b > 2 and f be Lebesgue measurable on 2 2 p D. If |f (z)| (1−|z| ) dm(z) belongs to CMp then |Ta,b f (z)|2 (1−|z|2 )p+2a−2 dm(z) also belongs to CMp .

Isomorphism, Decomposition and Discreteness Accordingly, the operator T is bounded from L2 (D) to L2 (D). Once the function f in Tf is replaced by g(w) = (1 − |w|2 )p/2 |f (w)|1S(2I) (w), where 1E stands for the characteristic function of E, we find 2 Int1 g(w)k(z, w) dm(w) D D dm(z) D |g(z)|2 dm(z) |I|p µf,p CMp . To handle Int2 , we note that both 2n |I| |1 − wz|, ¯ z ∈ S(I), w ∈ S(2n+1 I) \ S(2n I), and S(2n I) (1 − |z|2 )c−2 dm(z) (2n |I|)c , c > 1, hold for all n ∈ N ∪ {0}. When writing ∞ S(2n+1 I) \ S(2n I), D \ S(2I) = n=1 and using a > (2 − p)/2 as well as p ∈ (0, 2), we then get by the H¨ older inequality Int2 ∞ S(I) n=1 S(2n+1 I)\S(2n I) ∞ −(a+b) (2 |I|) n S(I) S(2n+1 I) n=1 2a+p ∞ |I| |I| ∞ S(2n+1 I) −a− p 2 (2 |I|) n 2 |f (w)| dm(w) (1 − |w|2 )1−b −(a+b) (2 |I|) n n=1 2a+p |f (w)|(1 − |w|2 )b−1 dm(w) |1 − wz| ¯ a+b µf,p S(2 2 |f (w)| dm(w) (1 − |w|2 )1−b n+1 I) 1 2 dm(z) (1 − |z|2 )2−p−2a dm(z) (1 − |z|2 )2−p−2a 2 2 n=1 ∞ |I|p 2−na 2 µf,p CMp .

Download PDF sample

Rated 4.51 of 5 – based on 8 votes