A NULLSTELLENSATZ FOR AMOEBAS

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552 ASTALA, CLOP, MATEU, OROBITG, and URIARTE-TUERO and consequently, we can write f = 1 z ∗ µ = R(I 1 ∗ µ) = I 1−α ∗ R(I α ∗ µ), where R is a Calderón-Zygmund operator and ‖f ‖ Ẇ 1−α,q =‖R(I α ∗µ)‖ q ‖I α ∗µ‖ q . For the converse, let f = I 1−α ∗ g be an admissible function for γ 1−α,q .Wehave that, up to a multiplicative constant, T = ∂f is an admissible distribution for Ċ α,p because I α ∗ T = R t (g), where R t is the transpose of R. Thus Ċ α,p (E) 1/p ≥|〈T,1〉| = |f ′ (∞)|, and the proof is complete. We end up with new quasiconformal invariants built on the Riesz capacities. THEOREM 2.10 Let φ : C → C be a principal K-quasiconformal mapping of the plane which is conformal on C \ E.Let1
DISTORTION OF HAUSDORFF MEASURES AND REMOVABILITY 553 are compact sets F such that Ċ α,p (F ) = 0 and H h (F ) > 0 for some measure function h(t) = t p ε(t). Thus Theorem 2.10 does not help with Conjecture 2.3. Wehavetobe content with the following setup. Given 1
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A NULLSTELLENSATZ FOR AMOEBAS KEVIN
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A NULLSTELLENSATZ FOR AMOEBAS 421 f
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A NULLSTELLENSATZ FOR AMOEBAS 443 C
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A NULLSTELLENSATZ FOR AMOEBAS 445 R
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448 DAVID GINZBURG The method we us
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450 DAVID GINZBURG Let ν denote a
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452 DAVID GINZBURG Proof The proof
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454 DAVID GINZBURG correspond to th
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456 DAVID GINZBURG Next, consider t
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458 DAVID GINZBURG To state the fol
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460 DAVID GINZBURG check that up to
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462 DAVID GINZBURG where L τ (¯s)
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464 DAVID GINZBURG To define the li
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466 DAVID GINZBURG cuspidality of t
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468 DAVID GINZBURG immediately foll
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470 DAVID GINZBURG expansion. Here
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472 DAVID GINZBURG Notice that S l
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474 DAVID GINZBURG values of m ′
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476 DAVID GINZBURG For 1 ≤ i ≤
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478 DAVID GINZBURG 2m rows, we have
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480 DAVID GINZBURG left to right. C
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482 DAVID GINZBURG unipotent orbit
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484 DAVID GINZBURG for every choice
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486 DAVID GINZBURG is equal to L(σ
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488 DAVID GINZBURG Here f π (h) is
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490 DAVID GINZBURG character ψ Um
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492 DAVID GINZBURG Proof The proof
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494 DAVID GINZBURG in the above ref
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496 DAVID GINZBURG THEOREM 7 The ir
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498 DAVID GINZBURG In the above, th
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Page 95 and 96: 502 DAVID GINZBURG [GP] S. GELBART
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A NULLSTELLENSATZ FOR AMOEBAS

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