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Limiting Reiteration for Real Interpolation and Optimal Sobolev Embeddings

Thesis Info

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External Link

Author

Irshaad Ahmed

Supervisor

Georgi Eremiev Karadzhov

Program

PhD

Institute

Government College University

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2006

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/handle/123456789/2037

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726583618

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Firstly, sharp reiteration theorems for the K−interpolation method in limiting cases are proved using two-sided estimates of the K−functional. As an application, sharp mapping properties of the Riesz potential are derived in a limiting case. Secondly, we prove optimal embeddings of the homogeneous Sobolev spaces built-up over function spaces in R n with K−monotone and rearrangement invariant norm into another rearrangement invariant function spaces. The investigation is based on pointwise and integral estimates of the rearrangement or the oscillation of the rearrangement of f in terms of the rearrangement of the derivatives of f .
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مُلّا جان محمد

مُلاّ جان محمد
افسوس ہے گذشتہ مہینہ ہمارے دومخلص قومی کارکن ملاجان محمدکلکتہ اورمولانا محمد عاقل الٰہ آباد انتقال کرگئے۔ملا صاحب کااصل وطن پشاور تھالیکن عرصہ دراز سے کلکتہ میں آبسے تھے اوراب سچ مچ وہی ان کاوطن تھا۔نہایت پُرجوش،جری اوربیباک انسان تھے۔گذشتہ نصف صدی میں کوئی قومی اور ملی تحریک ایسی نہیں ہے جس میں انہوں نے بڑھ چڑھ کراورولولہ و عزم کے ساتھ حصہ نہ لیا ہو۔ ان کی علمی زندگی کاآغاز تحریک خلافت سے ہوا اوراختتام مجلس مشاورت پر۔کلکتہ میں شاید ہی کوئی مسلم ادارہ(یہاں تک کہ محمڈن اسپورٹنگ کلب بھی) ایسا ہوجس میں ملاصاحب نے نمایاں حصہ نہ لیاہو۔اسی وجہ سے وہ کلکتہ کے لوگوں میں بے حد مقبول تھے۔ بڑے بے غرض،بے لوث اورنہایت سادہ اورمخلص مسلمان تھے۔۱۹۵۰ء میں کلکتہ کے فساد میں لوگوں نے ان کو بچوں کی طرح چیختے اور روتے دیکھا ہے۔ عمر۸۵ سال کے قریب تھی۔ [نومبر ۱۹۷۲]

 

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