There are many ahadith and much that can be said in regard to what took place for Lady Fatimah after the Prophet's demise, but we will only examine one hadith from Sahih Bukhari, the most reliable source of Sunnis, in the detailed answer.
There are many ahadith and much that can be said in regard to what took place for Lady Fatimah after the Prophet's demise. However some of the details may not be accepted by our Sunni brothers, but no one can entirely deny these incidents taking place.
In this regard, we will examine a hadith from Sahih Bukhari, the most authentic source of Sunnis:
" ان فاطمه ابنة رسول الله سألت ابا بکر الصدیق بعد وفاة رسول الله (ص) أن یقسم لها میراثها ما ترک رسول الله ص مما أفاء الله علیه فقال لها أبوبکر أن رسول الله ص قال لا نورث ما ترکنا صدقة فغضبت فاطمة بنت رسول الله فهجرت أبا بکر فلم تزل مهاجرته حتی توفیت ";  Lady Fatimah, the prophet's daughter, asked the first Caliph for her inheritance. Abu Bakr claimed that the Prophet once stated: "We [the prophets] do not leave any inheritance behind, and what we leave behind is charity!" Upon hearing this answer, Lady Fatimah became angry at Abu Bakr and didn’t speak with him anymore and their relationship stayed that way until her demise.
We know that there is another hadith from the Prophet, also narrated in Sahih Bukhari, which clearly declares that one who upsets Fatimah is like a person who upsets the prophet. 
These two ahadith, which are accepted by all Islamic sects, are enough to prove the Shia's belief of Lady Fatimah being oppressed.
For more information about Sunni and Shiah books that are related to the history of Lady Fatimah, in addition to referring to Question 11074(website: 10926), you can refer to other websites dedicated to this field.