| 要約: | Vector-valued analytic functions in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">C</mi><mi>n</mi></msup></semantics></math></inline-formula>, which are known to have vector-valued tempered distributional boundary values, are shown to be in the Hardy space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>H</mi><mi>p</mi></msup><mo>,</mo><mspace width="0.277778em"></mspace><mn>1</mn><mo>≤</mo><mi>p</mi><mo><</mo><mn>2</mn></mrow></semantics></math></inline-formula>, if the boundary value is in the vector-valued <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>L</mi><mi>p</mi></msup><mo>,</mo><mspace width="0.277778em"></mspace><mn>1</mn><mo>≤</mo><mi>p</mi><mo><</mo><mn>2</mn></mrow></semantics></math></inline-formula>, functions. The analysis of this paper extends the analysis of a previous paper that considered the cases for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mo>≤</mo><mi>p</mi><mo>≤</mo><mo>∞</mo></mrow></semantics></math></inline-formula>. Thus, with the addition of the results of this paper, the considered problems are proved for all <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>,</mo><mspace width="0.277778em"></mspace><mn>1</mn><mo>≤</mo><mi>p</mi><mo>≤</mo><mo>∞</mo></mrow></semantics></math></inline-formula>.
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