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• W2068047231 abstract "We prove that there exist <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=n> <mml:semantics> <mml:mi>n</mml:mi> <mml:annotation encoding=application/x-tex>n</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-homogeneous polynomials <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=p Subscript n> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi>p</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:mrow> <mml:annotation encoding=application/x-tex>{p_n}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> on a complex <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=d> <mml:semantics> <mml:mi>d</mml:mi> <mml:annotation encoding=application/x-tex>d</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-dimensional ball such that <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=double-vertical-bar p Subscript n Baseline double-vertical-bar Subscript normal infinity Baseline equals 1> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mrow> <mml:mo symmetric=true>‖</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi>p</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:mrow> </mml:mrow> <mml:mo symmetric=true>‖</mml:mo> </mml:mrow> <mml:mi mathvariant=normal>∞<!-- ∞ --></mml:mi> </mml:msub> </mml:mrow> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>{left | {{p_n}} right |_infty } = 1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=double-vertical-bar p Subscript n Baseline double-vertical-bar Subscript 2 Baseline greater-than-or-slanted-equals StartRoot pi EndRoot 2 Superscript negative d> <mml:semantics> <mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mrow> <mml:mo symmetric=true>‖</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi>p</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:mrow> </mml:mrow> <mml:mo symmetric=true>‖</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> <mml:mo>⩾<!-- ⩾ --></mml:mo> <mml:msqrt> <mml:mi>π<!-- π --></mml:mi> </mml:msqrt> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msup> <mml:mn>2</mml:mn> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>−<!-- − --></mml:mo> <mml:mi>d</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> </mml:mrow> <mml:annotation encoding=application/x-tex>{left | {{p_n}} right |_2} geqslant sqrt pi {2^{- d}}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. This enables us to answer some questions about <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper H Subscript p> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi>H</mml:mi> <mml:mi>p</mml:mi> </mml:msub> </mml:mrow> <mml:annotation encoding=application/x-tex>{H_p}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and Bloch spaces on a complex ball. We also investigate interpolation by <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=n> <mml:semantics> <mml:mi>n</mml:mi> <mml:annotation encoding=application/x-tex>n</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-homogeneous polynomials on a <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=2> <mml:semantics> <mml:mn>2</mml:mn> <mml:annotation encoding=application/x-tex>2</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-dimensional complex ball." @default.
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• W2068047231 title "On homogeneous polynomials on a complex ball" @default.
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