A Real Variable Method for the Cauchy Transform and Applications to Analytic CapacityNagoya University, Department of Mathematics, College of General Education, 1987 - Analytic functions - 133 pages |
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Page 50
... lemmas necessary for the proof . Here are n Lemma 2.10 ( Calderón [ 4 ] ) . || I [ a ] || 2 , 2 ≤ ( Const ) || a || ( n ≥ 1 ) . Proof . Fixing 0 < < 1/2 , we put s [ a ] ( x , y ) = ( x - y ) [ a ] ( x , y ) . ε Since ( S [ a ] ...
... lemmas necessary for the proof . Here are n Lemma 2.10 ( Calderón [ 4 ] ) . || I [ a ] || 2 , 2 ≤ ( Const ) || a || ( n ≥ 1 ) . Proof . Fixing 0 < < 1/2 , we put s [ a ] ( x , y ) = ( x - y ) [ a ] ( x , y ) . ε Since ( S [ a ] ...
Page 91
... Lemmas 3.4 and 3.6 show that Ĉ ( n ) < ∞ for all n ≥ 1. By Lemmas 3.4 and 3.5 , we have , for any non - negative ... necessary for the proof . Lemma -91- Proof of the latter half of Theorem 5.
... Lemmas 3.4 and 3.6 show that Ĉ ( n ) < ∞ for all n ≥ 1. By Lemmas 3.4 and 3.5 , we have , for any non - negative ... necessary for the proof . Lemma -91- Proof of the latter half of Theorem 5.
Page 92
Takafumi Murai. Here are two lemmas necessary for the proof . Lemma 3.7 . Proof . Let = I To ( 1 ) = la - B12 / 100 . ᄒ ( 1 ) x € [ ( k − 1 ) 2 ̃a , k2 ̃¶ ) ( k 。 is odd ) . 1 +1 x16 ( x ) 1 +10 · la 1a - 312-9 = 1 = | a8 | 29 | Re N ...
Takafumi Murai. Here are two lemmas necessary for the proof . Lemma 3.7 . Proof . Let = I To ( 1 ) = la - B12 / 100 . ᄒ ( 1 ) x € [ ( k − 1 ) 2 ̃a , k2 ̃¶ ) ( k 。 is odd ) . 1 +1 x16 ( x ) 1 +10 · la 1a - 312-9 = 1 = | a8 | 29 | Re N ...
Common terms and phrases
² dx absolute constant analytic capacity analytic functions anti-symmetric Banach space C₂ Calderón Carleson measure Cauchy transform Cg wg chord-arc curve compact set completes the proof component Const G Const mo Cotlar's lemma crank of degree curve with constant deduce ds dt dx dy dy ds dyadic interval estimate exists finite Galton-Watson process graph H₂ Hence infimum integer L₁ lemmas necessary locally chord-arc Lreal Lreal,1 manner midpoint mutually disjoint n-tuple non-negative function norm obtain oc(B open set positive integer pr(E proof of Theorem real-valued required inequality RSL of Type segments sequence shows singular integral operator Tx-y VII Const VII VII Vlog w₁ x)dx yields δ δ δε Σ Σ дх շո है